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{"id":25820,"date":"2023-05-21T08:49:29","date_gmt":"2023-05-21T07:49:29","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25820"},"modified":"2023-05-21T12:26:13","modified_gmt":"2023-05-21T11:26:13","slug":"um-sistema-de-equacoes-escrito-no-caderno-da-joana","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25820","title":{"rendered":"Um sistema de equa\u00e7\u00f5es escrito no caderno da Joana"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25820' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25820' class='GTTabs_curr'><a  id=\"25820_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25820' ><a  id=\"25820_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_25820'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera o sistema de equa\u00e7\u00f5es escrito no caderno da Joana.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25821\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25821\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10.png\" data-orig-size=\"303,217\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag199-T10\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10.png\" class=\"aligncenter wp-image-25821\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10-300x215.png\" alt=\"\" width=\"240\" height=\"172\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10-300x215.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10.png 303w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<ol>\n<li>Resolve uma das equa\u00e7\u00f5es em ordem a uma das inc\u00f3gnitas.<br \/>Escolhe bem a equa\u00e7\u00e3o por onde queres come\u00e7ar de modo a facilitar os c\u00e1lculos.<\/li>\n<li>Substitui, na outra equa\u00e7\u00e3o, essa inc\u00f3gnita pela express\u00e3o obtida.<\/li>\n<li>Resolve a equa\u00e7\u00e3o que ficou s\u00f3 com uma inc\u00f3gnita.<br \/>Que valor obtiveste?<\/li>\n<li>Substitui o valor encontrado na primeira equa\u00e7\u00e3o.<\/li>\n<li>Escreve o par ordenado que \u00e9 solu\u00e7\u00e3o do sistema.<\/li>\n<li>Verifica graficamente se a solu\u00e7\u00e3o obtida est\u00e1 correta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25820' onClick='GTTabs_show(1,25820)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25820'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Considera o sistema de equa\u00e7\u00f5es escrito no caderno da Joana.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25821\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25821\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10.png\" data-orig-size=\"303,217\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag199-T10\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10.png\" class=\"wp-image-25821 alignright\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10-300x215.png\" alt=\"\" width=\"240\" height=\"172\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10-300x215.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10.png 303w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<ol>\n<li>Resolve uma das equa\u00e7\u00f5es em ordem a uma das inc\u00f3gnitas.<br \/>Escolhe bem a equa\u00e7\u00e3o por onde queres come\u00e7ar de modo a facilitar os c\u00e1lculos.<\/li>\n<li>Substitui, na outra equa\u00e7\u00e3o, essa inc\u00f3gnita pela express\u00e3o obtida.<\/li>\n<li>Resolve a equa\u00e7\u00e3o que ficou s\u00f3 com uma inc\u00f3gnita.<br \/>Que valor obtiveste?<\/li>\n<li>Substitui o valor encontrado na primeira equa\u00e7\u00e3o.<\/li>\n<li>Escreve o par ordenado que \u00e9 solu\u00e7\u00e3o do sistema.<\/li>\n<li>Verifica graficamente se a solu\u00e7\u00e3o obtida est\u00e1 correta.<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 10%; background-color: #a9e8de;\" rowspan=\"2\"><strong>Ponto<\/strong><\/td>\n<td style=\"width: 45%; background-color: #a9e8de;\"><strong>1.\u00aa equa\u00e7\u00e3o<\/strong><\/td>\n<td style=\"width: 45%; background-color: #a9e8de;\"><strong>2.\u00aa equa\u00e7\u00e3o<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 37.6302%; background-color: #a9e8de;\"><strong>\\( &#8211; 2x + y = &#8211; 1\\)<\/strong><\/td>\n<td style=\"width: 55.599%; background-color: #a9e8de;\"><strong>\\( &#8211; x + 2y = 4\\)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top; width: 5.72917%;\">1.<\/td>\n<td style=\"width: 37.6302%;\">\\(\\begin{array}{*{20}{c}}{ &#8211; 2x + y = &#8211; 1}&amp; \\Leftrightarrow &amp;{y = 2x &#8211; 1}\\end{array}\\)<\/td>\n<td style=\"width: 55.599%;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top; width: 5.72917%;\">2.<\/td>\n<td style=\"width: 37.6302%;\">\u00a0<\/td>\n<td style=\"width: 55.599%;\">\\( &#8211; x + 2\\left( {2x &#8211; 1} \\right) = 4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top; width: 5.72917%;\">3.<\/td>\n<td style=\"width: 37.6302%;\">\u00a0<\/td>\n<td style=\"width: 55.599%;\">\\(\\begin{array}{*{20}{l}}{ &#8211; x + 2\\left( {2x &#8211; 1} \\right) = 4}&amp; \\Leftrightarrow &amp;{ &#8211; x + 4x &#8211; 2 = 4}\\\\{}&amp; \\Leftrightarrow &amp;{3x = 6}\\\\{}&amp; \\Leftrightarrow &amp;{x = 2}\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top; width: 5.72917%;\">4.<\/td>\n<td style=\"width: 37.6302%;\">\\(\\begin{array}{*{20}{c}}{y = 2 \\times 2 &#8211; 1}&amp; \\Leftrightarrow &amp;{y = 3}\\end{array}\\)<\/td>\n<td style=\"width: 55.599%;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top; width: 5.72917%;\">5.<\/td>\n<td style=\"width: 93.2292%;\" colspan=\"2\">\\(\\left( {2,3} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top; width: 5.72917%;\">6.<\/td>\n<td style=\"width: 93.2292%;\" colspan=\"2\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10_Grafico.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25840\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25840\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10_Grafico.png\" data-orig-size=\"921,787\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag199-T10_Grafico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10_Grafico.png\" class=\"alignnone wp-image-25840\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10_Grafico-300x256.png\" alt=\"\" width=\"640\" height=\"547\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10_Grafico-300x256.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10_Grafico-768x656.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10_Grafico.png 921w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25820' onClick='GTTabs_show(0,25820)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera o sistema de equa\u00e7\u00f5es escrito no caderno da Joana. Resolve uma das equa\u00e7\u00f5es em ordem a uma das inc\u00f3gnitas.Escolhe bem a equa\u00e7\u00e3o por onde queres come\u00e7ar de modo a facilitar&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25822,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,344,239],"series":[],"class_list":["post-25820","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-funcao-afim","tag-grafico","tag-sistema-de-equacoes"],"views":86,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag199-T10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25820","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=25820"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25820\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25822"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25820"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25820"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25820"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25820"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}