{"id":128027,"date":"2021-05-26T07:00:00","date_gmt":"2021-05-26T10:00:00","guid":{"rendered":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/?post_type=ensino_fundamental&#038;p=128027"},"modified":"2021-12-22T12:02:28","modified_gmt":"2021-12-22T14:02:28","slug":"matematica-equacoes-e-sistema-de-equacoes-polinomiais-do-primeiro-grau","status":"publish","type":"ensino_fundamental","link":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/ensino_fundamental\/matematica-equacoes-e-sistema-de-equacoes-polinomiais-do-primeiro-grau\/","title":{"rendered":"Matem\u00e1tica &#8211; Equa\u00e7\u00f5es e Sistema de Equa\u00e7\u00f5es polinomiais do primeiro grau"},"content":{"rendered":"\n<p class=\"has-text-align-center has-black-color has-light-green-cyan-background-color has-text-color has-background\" style=\"font-size:22px\">Ol\u00e1, estudante! Esta videoaula de Matem\u00e1tica para o <strong>8\u00ba ano do Ensino Fundamental <\/strong>foi veiculada na TV no dia <strong>26\/05\/2021 (Quarta-feira)<\/strong>. Aqui no Portal Conex\u00e3o Escola, ela est\u00e1 dispon\u00edvel juntamente com a proposta de atividade.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/1-4-e1622038186690.jpg\" alt=\"\" class=\"wp-image-128028\" width=\"443\" height=\"402\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/1-4-e1622038186690.jpg 344w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/1-4-e1622038186690-300x272.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><figcaption><strong>Fonte:  <a href=\"https:\/\/pixabay.com\/pt\/illustrations\/search\/equation\/\">https:\/\/pixabay.com\/pt\/illustrations\/search\/equation\/<\/a><\/strong><\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-white-color has-luminous-vivid-orange-background-color has-text-color has-background has-medium-font-size\">Ol\u00e1 estudante do 8\u00ba ano, nesta atividade voc\u00ea ir\u00e1 estudar sobre as equa\u00e7\u00f5es polinomiais do primeiro grau, aprofundando os conhecimentos em equa\u00e7\u00f5es com duas vari\u00e1veis e represent\u00e1-las como um sistema de equa\u00e7\u00f5es, mostrando a rela\u00e7\u00e3o de depend\u00eancia entre uma e outra, al\u00e9m de fazer resolu\u00e7\u00f5es gr\u00e1ficas desse tipo de sistema de equa\u00e7\u00e3o.<\/p>\n\n\n\n<p class=\"has-text-align-center has-white-color has-luminous-vivid-orange-background-color has-text-color has-background\" style=\"font-size:29px\">Venha iniciar seus estudos, voc\u00ea n\u00e3o pode ficar fora dessa!<\/p>\n\n\n\n<p class=\"has-text-align-center has-white-color has-black-background-color has-text-color has-background\" style=\"font-size:23px\">Assista a videoaula a seguir com a tem\u00e1tica: Equa\u00e7\u00f5es e Sistema de Equa\u00e7\u00f5es polinomiais do primeiro grau&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<p class=\"responsive-video-wrap clr\"><iframe title=\"Matem\u00e1tica - 8 ano\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/vD283QwQ0c0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<\/div><figcaption><strong>Agrupamento  H|8\u00ba ano|Ciclo da adolesc\u00eancia |Matem\u00e1tica | Prof. Bruno Silva Silvestre<\/strong><\/figcaption><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-text-align-center has-white-color has-vivid-red-background-color has-text-color has-background\" style=\"font-size:22px\">Ol\u00e1, nesta atividade de matem\u00e1tica voc\u00ea vai estudar sobre as equa\u00e7\u00f5es e sistema de equa\u00e7\u00f5es polinomiais do primeiro grau, ressaltando:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-red-color\">Formas de resolver uma equa\u00e7\u00e3o polinomial do primeiro grau;<\/span><\/strong><\/li><li><strong><span class=\"has-inline-color has-vivid-red-color\">Situa\u00e7\u00f5es problemas envolvendo equa\u00e7\u00f5es;<\/span><\/strong><\/li><li><strong><span class=\"has-inline-color has-vivid-red-color\">Sistema de equa\u00e7\u00f5es com duas vari\u00e1veis;<\/span><\/strong><\/li><li><strong><span class=\"has-inline-color has-vivid-red-color\">M\u00e9todos de resolu\u00e7\u00e3o de um sistema de equa\u00e7\u00f5es;<\/span><\/strong><\/li><li><strong><span class=\"has-inline-color has-vivid-red-color\">Resolu\u00e7\u00e3o gr\u00e1fica de um sistema de equa\u00e7\u00f5es.<\/span><\/strong><\/li><\/ul>\n\n\n\n<p class=\"has-medium-font-size\">Para iniciar seus estudos \u00e9 importante lembrar que a equa\u00e7\u00e3o faz parte de um estudo maior que refere-se \u00e0 \u00e1lgebra, acompanhe a explica\u00e7\u00e3o sobre o que \u00e9 uma equa\u00e7\u00e3o:<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Equa\u00e7\u00e3o<\/strong> \u00e9 uma senten\u00e7a matem\u00e1tica expressa por uma igualdade em que h\u00e1 pelo menos uma letra que representa um valor desconhecido, chamada inc\u00f3gnita. Resolver uma equa\u00e7\u00e3o \u00e9 determinar o <strong>valor desconhecido da inc\u00f3gnita<\/strong>, ou seja, obter a <strong>solu\u00e7\u00e3o<\/strong> ou a<strong> raiz<\/strong> da equa\u00e7\u00e3o.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Para exemplificar o contexto de uma equa\u00e7\u00e3o observe o exemplo a seguir:<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Exemplo1<\/strong>:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Rafael possui R $43,50, sendo R$17,50 em moedas e o restante em c\u00e9dulas de 2 reais.&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/2-3-e1622038253166.jpg\" alt=\"\" class=\"wp-image-128029\" width=\"403\" height=\"340\"\/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 112) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Podemos determinar, por meio de uma equa\u00e7\u00e3o, quantas c\u00e9dulas de 2 reais Rafael possui. Para isso, indicamos por x a quantidade de c\u00e9dulas de 2 reais e escrevemos a equa\u00e7\u00e3o:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/3-5-e1622038269489.jpg\" alt=\"\" class=\"wp-image-128030\" width=\"637\" height=\"300\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/3-5-e1622038269489.jpg 392w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/3-5-e1622038269489-300x142.jpg 300w\" sizes=\"(max-width: 637px) 100vw, 637px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 112) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Podemos resolver essa equa\u00e7\u00e3o utilizando os <strong>princ\u00edpios aditivo e multiplicativo da igualdade<\/strong>.&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Lembre-se de que pelo princ\u00edpio aditivo a igualdade se mant\u00e9m ao adicionarmos ou ao subtrairmos um mesmo n\u00famero dos dois membros de uma equa\u00e7\u00e3o. E pelo princ\u00edpio multiplicativo, a igualdade se mant\u00e9m ao multiplicarmos ou dividirmos os dois membros da equa\u00e7\u00e3o pelo mesmo n\u00famero diferente de zero.&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/4-5-e1622038281229.jpg\" alt=\"\" class=\"wp-image-128031\" width=\"695\" height=\"248\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/4-5-e1622038281229.jpg 544w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/4-5-e1622038281229-300x107.jpg 300w\" sizes=\"(max-width: 695px) 100vw, 695px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 112) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Portanto, Rafael possui 13 c\u00e9dulas de 2 reais.<\/p>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background\" style=\"font-size:22px\">Agora \u00e9 a sua vez!<\/p>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background has-medium-font-size\"><strong>Quest\u00e3o 01<\/strong>. A balan\u00e7a a seguir est\u00e1 em equil\u00edbrio. Nela, as caixas azuis possuem massas com a mesma medida. Sabendo que nessas balan\u00e7as, caixas de mesma cor possuem medidas de massa iguais, elabore uma equa\u00e7\u00e3o e resolva-a em cada um dos casos:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/5-4-e1622038295581.jpg\" alt=\"\" class=\"wp-image-128032\" width=\"582\" height=\"289\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/5-4-e1622038295581.jpg 397w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/5-4-e1622038295581-300x149.jpg 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 113) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/6-4-e1622038307886.jpg\" alt=\"\" class=\"wp-image-128033\" width=\"518\" height=\"281\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/6-4-e1622038307886.jpg 370w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/6-4-e1622038307886-300x163.jpg 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 113) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/7-5-e1622038320892.jpg\" alt=\"\" class=\"wp-image-128034\" width=\"538\" height=\"294\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/7-5-e1622038320892.jpg 344w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/7-5-e1622038320892-300x164.jpg 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 113) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background\" style=\"font-size:22px\"><strong>Quest\u00e3o 02<\/strong>. Nat\u00e1lia pagou R $315,00 pelas tr\u00eas pe\u00e7as de roupa a seguir.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/8-4-e1622038332747.jpg\" alt=\"\" class=\"wp-image-128035\" width=\"564\" height=\"293\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/8-4-e1622038332747.jpg 423w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/8-4-e1622038332747-300x155.jpg 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><figcaption><strong>Fonte: (PATARO &amp; BALESTRI, 2018, p. 114) PNLD<\/strong><\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Sabendo que as cal\u00e7as t\u00eam pre\u00e7os iguais e que a saia custou metade do pre\u00e7o da cal\u00e7a:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">a) escreva uma equa\u00e7\u00e3o que represente essa situa\u00e7\u00e3o.&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">b) determine o pre\u00e7o pago por Nat\u00e1lia em cada pe\u00e7a de roupa.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Agora que voc\u00ea j\u00e1 sabe o que \u00e9 uma equa\u00e7\u00e3o do primeiro grau, inclusive consegue resolv\u00ea-la, vamos ampliar nossos estudos para equa\u00e7\u00f5es do primeiro grau com duas vari\u00e1veis.<\/p>\n\n\n\n<p class=\"has-white-color has-luminous-vivid-orange-background-color has-text-color has-background\" style=\"font-size:23px\">Para come\u00e7ar esse estudo, acompanhe a situa\u00e7\u00e3o a seguir:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/9-4-e1622038344741.jpg\" alt=\"\" class=\"wp-image-128036\" width=\"764\" height=\"330\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/9-4-e1622038344741.jpg 554w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/9-4-e1622038344741-300x129.jpg 300w\" sizes=\"(max-width: 764px) 100vw, 764px\" \/><figcaption><strong>Fonte: (PATARO &amp; BALESTRI, 2018, p. 115) PNLD<\/strong><\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Podemos resolver esse problema utilizando uma equa\u00e7\u00e3o. Para isso, indicamos por x e por y os n\u00fameros procurados.&nbsp;<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>x + y = 6&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">A seguir, temos alguns poss\u00edveis valores de x e de y.&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/10-3-e1622038356408.jpg\" alt=\"\" class=\"wp-image-128037\" width=\"445\" height=\"364\"\/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 115) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\">As solu\u00e7\u00f5es de uma equa\u00e7\u00e3o do 1o grau com duas inc\u00f3gnitas s\u00e3o pares ordenados. Em rela\u00e7\u00e3o \u00e0 equa\u00e7\u00e3o x + y = 6 , os pares ordenados (6, 0) , (5, 1) , (4, 2) , (3, 3) , (2, 4) , (1, 5) e (0,6) s\u00e3o algumas de suas solu\u00e7\u00f5es.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/11-3-e1622038374742.jpg\" alt=\"\" class=\"wp-image-128038\" width=\"490\" height=\"458\"\/><figcaption><strong>Fonte: (PATARO &amp; BALESTRI, 2018, p. 115) PNLD<\/strong><\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Note que se ligarmos cada um dos pontos obtidos com as coordenadas que eram solu\u00e7\u00e3o da equa\u00e7\u00e3o, tem-se uma reta:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/12-3-e1622038385574.jpg\" alt=\"\" class=\"wp-image-128039\" width=\"498\" height=\"435\"\/><figcaption><strong>Fonte: (PATARO &amp; BALESTRI, 2018, p. 115) PNLD<\/strong><\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background\" style=\"font-size:22px\">Agora \u00e9 com voc\u00ea!<\/p>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background\" style=\"font-size:22px\"><strong>Quest\u00e3o 03<\/strong>. Observe a reta formada no plano cartesiano:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/13-3-e1622038398485.jpg\" alt=\"\" class=\"wp-image-128040\" width=\"463\" height=\"393\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/13-3-e1622038398485.jpg 316w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/13-3-e1622038398485-300x254.jpg 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><figcaption><strong>Fonte: (PATARO &amp; BALESTRI, 2018, p. 115) PNLD<\/strong><\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-vivid-red-color has-cyan-bluish-gray-background-color has-text-color has-background\" style=\"font-size:23px\">Essa reta representa as solu\u00e7\u00f5es de qual das equa\u00e7\u00f5es?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/14-2-e1622038409341.jpg\" alt=\"\" class=\"wp-image-128041\" width=\"273\" height=\"238\"\/><\/figure>\n\n\n\n<p class=\"has-medium-font-size\">Agora vamos ver quando se duas equa\u00e7\u00f5es com duas vari\u00e1veis cada uma, estudando o conceito matem\u00e1tico de <strong>sistemas de equa\u00e7\u00f5es<\/strong>.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Para aprofundar os estudos nos sistemas de equa\u00e7\u00f5es observe com aten\u00e7\u00e3o a situa\u00e7\u00e3o a seguir:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Em um estacionamento, entre carros e motos, h\u00e1 12 ve\u00edculos, sendo a maioria carros. A diferen\u00e7a entre a quantidade de carros e o dobro da quantidade de motos \u00e9 igual a 3. <\/p>\n\n\n\n<p class=\"has-vivid-red-color has-cyan-bluish-gray-background-color has-text-color has-background\" style=\"font-size:23px\">Quantos carros e quantas motos h\u00e1 nesse estacionamento?<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/15-2-e1622038421945.jpg\" alt=\"\" class=\"wp-image-128042\" width=\"630\" height=\"416\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/15-2-e1622038421945.jpg 395w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/15-2-e1622038421945-300x198.jpg 300w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 118) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Podemos resolver essa quest\u00e3o escrevendo duas equa\u00e7\u00f5es: uma para representar a quantidade total de ve\u00edculos no estacionamento e outra para representar a diferen\u00e7a entre a quantidade de carros e o dobro da quantidade de motos. <\/p>\n\n\n\n<p class=\"has-vivid-red-color has-cyan-bluish-gray-background-color has-text-color has-background\" style=\"font-size:23px\">Para isso, chamamos de x a quantidade de carros e de y a quantidade de motos.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/16-2-e1622038433856.jpg\" alt=\"\" class=\"wp-image-128043\" width=\"659\" height=\"184\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/16-2-e1622038433856.jpg 438w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/16-2-e1622038433856-300x84.jpg 300w\" sizes=\"(max-width: 659px) 100vw, 659px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 118) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-vivid-red-color has-cyan-bluish-gray-background-color has-text-color has-background\" style=\"font-size:23px\">Indicamos o sistema de equa\u00e7\u00f5es da seguinte forma:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/17-2-e1622038446692.jpg\" alt=\"\" class=\"wp-image-128044\" width=\"249\" height=\"144\"\/><\/figure>\n\n\n\n<p class=\"has-vivid-red-color has-cyan-bluish-gray-background-color has-text-color has-background\" style=\"font-size:23px\">Para resolver esse sistema, pode-se utilizar o m\u00e9todo da substitui\u00e7\u00e3o:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/18-2-e1622038458319.jpg\" alt=\"\" class=\"wp-image-128045\" width=\"657\" height=\"480\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/18-2-e1622038458319.jpg 552w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/18-2-e1622038458319-300x219.jpg 300w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/19-2-e1622038470787.jpg\" alt=\"\" class=\"wp-image-128046\" width=\"679\" height=\"338\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/19-2-e1622038470787.jpg 534w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/19-2-e1622038470787-300x149.jpg 300w\" sizes=\"(max-width: 679px) 100vw, 679px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-medium-font-size\">Perceba, que, se atribuirmos valores para cada uma das equa\u00e7\u00f5es, iremos ter v\u00e1rios pares ordenados, e se colocarmos no gr\u00e1fico os pontos obtidos em cada uma das equa\u00e7\u00f5es, as retas correspondentes a cada uma delas v\u00e3o ser concorrentes, ou seja, v\u00e3o se cruzar em um \u00fanico ponto, este, ponto \u00e9 o ponto exato da resolu\u00e7\u00e3o do sistema de equa\u00e7\u00f5es, j\u00e1 que \u00e9 o ponto comum da resolu\u00e7\u00e3o de uma e outra equa\u00e7\u00e3o ao mesmo tempo, satisfazendo as duas equa\u00e7\u00f5es.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/20-1-e1622038482461.jpg\" alt=\"\" class=\"wp-image-128047\" width=\"551\" height=\"458\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/20-1-e1622038482461.jpg 380w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/20-1-e1622038482461-300x249.jpg 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 118) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background\" style=\"font-size:22px\">Agora chegou a sua vez de colocar todos os estudos desta atividade em pr\u00e1tica, resolvendo as quest\u00f5es:<\/p>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background\" style=\"font-size:22px\"><strong>Quest\u00e3o 04<\/strong>. Leia o problema e, em seguida, responda \u00e0s perguntas:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/21-1-e1622038494422.jpg\" alt=\"\" class=\"wp-image-128048\" width=\"824\" height=\"454\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/21-1-e1622038494422.jpg 662w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/21-1-e1622038494422-300x165.jpg 300w\" sizes=\"(max-width: 824px) 100vw, 824px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 118) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background\" style=\"font-size:22px\"><strong>Quest\u00e3o 05<\/strong>. Adriana e Felipe possuem juntos a quantidade de CDs indicada na figura, sendo que Adriana possui 4 CDs a mais que Felipe. Chamando de x a quantidade de CDs de Adriana e de y a quantidade de CDs de Felipe, escreva um sistema de duas equa\u00e7\u00f5es do 1o grau com duas inc\u00f3gnitas que possibilite determinar a quantidade de CDs de cada um deles.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/22-1-e1622038506192.jpg\" alt=\"\" class=\"wp-image-128049\" width=\"590\" height=\"284\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/22-1-e1622038506192.jpg 351w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/22-1-e1622038506192-300x144.jpg 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><figcaption>Fonte: (PATARO &amp; BALESTRI, 2018, p. 118) PNLD<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background\" style=\"font-size:23px\"><strong>Quest\u00e3o 06<\/strong>. Qual dos gr\u00e1ficos mostra a solu\u00e7\u00e3o do sistema:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/23-e1622045042583.jpg\" alt=\"\" class=\"wp-image-128050\" width=\"298\" height=\"144\"\/><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/24-e1622045055495.jpg\" alt=\"\" class=\"wp-image-128051\" width=\"595\" height=\"533\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/24-e1622045055495.jpg 463w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/05\/24-e1622045055495-300x268.jpg 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-text-align-center has-white-color has-luminous-vivid-orange-background-color has-text-color has-background\" style=\"font-size:25px\">Parab\u00e9ns pelo empenho em resolver as quest\u00f5es propostas!<\/p>\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-large-font-size\"><strong>RELEMBRANDO!!!!!!!<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Nesta atividade de matem\u00e1tica, voc\u00ea estudou sobre os conhecimentos alg\u00e9bricos, sobretudo, sobre os conhecimentos de equa\u00e7\u00f5es do primeiro grau com uma e duas inc\u00f3gnitas. Percebeu que as equa\u00e7\u00f5es do primeiro grau com duas inc\u00f3gnitas podem ter infinitas respostas, por isso, o valor desconhecido delas \u00e9 chamado de vari\u00e1vel. J\u00e1 um sistema de equa\u00e7\u00f5es do primeiro grau pode ter apenas uma \u00fanica solu\u00e7\u00e3o que satisfa\u00e7a as duas equa\u00e7\u00f5es, por isso o seu valor desconhecido \u00e9 chamado de vari\u00e1vel. H\u00e1 casos espec\u00edficos que sistemas de equa\u00e7\u00f5es n\u00e3o geram um resultado, ou, h\u00e1 casos que todas as solu\u00e7\u00f5es de uma s\u00e3o tamb\u00e9m solu\u00e7\u00e3o da outra equa\u00e7\u00e3o, nas pr\u00f3ximas aulas exploraremos esses casos.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center has-white-color has-luminous-vivid-orange-background-color has-text-color has-background\" style=\"font-size:25px\">Parab\u00e9ns pelo estudo, continue se empenhando com as atividades do conex\u00e3o escola. At\u00e9 a pr\u00f3xima atividade de matem\u00e1tica!<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Habilidades&nbsp;<\/strong><\/td><td><strong>Habilidade Estruturante<\/strong><br><strong>(EF08MA08)<\/strong> Resolver e elaborar problemas relacionados ao seu contexto pr\u00f3ximo, que possam ser representados por sistemas de equa\u00e7\u00f5es de 1\u00ba grau com duas inc\u00f3gnitas e interpret\u00e1-los, utilizando, inclusive, o plano cartesiano como recurso.<br><strong>Habilidades complementares<\/strong><br><strong>EF08MA06-<\/strong><br><strong>E&nbsp;EF08MA07&nbsp;<\/strong><br><strong>GO-EF08MA28&nbsp;<\/strong><br><strong>EF08MA09<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Refer\u00eancias:<\/strong><\/td><td>DANTE, Luiz Roberto. <strong>Tel\u00e1ris matem\u00e1tica, 8\u00ba ano<\/strong>: ensino fundamental, anos finais &#8211; 3. ed. &#8211; S\u00e3o Paulo : \u00c1tica, 2018.&nbsp;PATARO, Patricia Moreno., BALESTRI, Rodrigo. <strong>Matem\u00e1tica essencial 8o ano <\/strong>: ensino fundamental, anos finais &#8211; 1. ed. &#8211; S\u00e3o Paulo : Scipione, 2018. PLND<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-cyan-bluish-gray-background-color has-background\" style=\"font-size:25px\">Professor, essa aula segue a Matriz Curricular das Habilidades Estruturantes 2021-2021. Foi elaborada no ano de 2020, com a suspens\u00e3o das aulas presenciais devido \u00e0 pandemia da Covid-19 e segue as orienta\u00e7\u00f5es de flexibiliza\u00e7\u00e3o curricular para o bi\u00eanio 2020\/2021 (Of\u00edcio Circular 147\/2020 Dirped).<\/p>\n","protected":false},"author":25,"featured_media":128028,"template":"","ef_categoria":[16,35],"ef_ano":[91],"ef_componente":[94],"class_list":["post-128027","ensino_fundamental","type-ensino_fundamental","status-publish","has-post-thumbnail","hentry","ef_categoria-ciclo-da-adolescencia-hi","ef_categoria-educacao-financeira-e-empreendedorismo-ciclo-da-adolescencia-hi","ef_ano-8o-ano","ef_componente-matematica","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/ensino_fundamental\/128027","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/ensino_fundamental"}],"about":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/types\/ensino_fundamental"}],"author":[{"embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/users\/25"}],"version-history":[{"count":0,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/ensino_fundamental\/128027\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media\/128028"}],"wp:attachment":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media?parent=128027"}],"wp:term":[{"taxonomy":"ef_categoria","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/ef_categoria?post=128027"},{"taxonomy":"ef_ano","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/ef_ano?post=128027"},{"taxonomy":"ef_componente","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/ef_componente?post=128027"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}