{"id":25769,"date":"2023-05-20T17:35:07","date_gmt":"2023-05-20T16:35:07","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25769"},"modified":"2023-05-20T19:39:48","modified_gmt":"2023-05-20T18:39:48","slug":"resolve-graficamente-os-sistemas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25769","title":{"rendered":"Resolve graficamente os sistemas"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25769' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25769' class='GTTabs_curr'><a  id=\"25769_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25769' ><a  id=\"25769_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_25769'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve graficamente os seguintes sistemas de equa\u00e7\u00f5es e classifica-os, justificando.<\/p>\n<ol>\n<li><br \/>\\(\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 7}\\\\{\\begin{array}{*{20}{l}}{x &#8211; y = 5}\\end{array}}\\end{array}} \\right.\\)<\/li>\n<li><br \/>\\(\\left\\{ {\\begin{array}{*{20}{l}}{x = 3 &#8211; y}\\\\{\\begin{array}{*{20}{l}}{2x + 2y = 4}\\end{array}}\\end{array}} \\right.\\)<\/li>\n<li><br \/>\\(\\left\\{ {\\begin{array}{*{20}{l}}{x = 6 &#8211; y}\\\\{\\begin{array}{*{20}{l}}{\\frac{1}{2}x + \\frac{1}{2}y = 3}\\end{array}}\\end{array}} \\right.\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25769' onClick='GTTabs_show(1,25769)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25769'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%; text-align: left;\">\n<p>\\(\\begin{array}{*{20}{c}}{\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 7}\\\\{\\begin{array}{*{20}{l}}{x &#8211; y = 5}\\end{array}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = &#8211; x + 7}\\\\{\\begin{array}{*{20}{l}}{y = x &#8211; 5}\\end{array}}\\end{array}} \\right.}\\end{array}\\)<\/p>\n<p>O sistema \u00e9 poss\u00edvel e determinado, pois as duas fun\u00e7\u00f5es afins possuem gr\u00e1ficos que s\u00e3o retas concorrentes, visto que possuem declives diferentes: \\( &#8211; 1\\) e \\(1\\).<\/p>\n<\/td>\n<td style=\"width: 50%;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25774\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25774\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5a.png\" data-orig-size=\"981,523\" 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_Pag197-5a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5a.png\" class=\"alignnone wp-image-25774\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5a-300x160.png\" alt=\"\" width=\"480\" height=\"256\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5a-300x160.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5a-768x409.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5a.png 981w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: left;\">\n<p>\\(\\begin{array}{*{20}{c}}{\\left\\{ {\\begin{array}{*{20}{l}}{x = 3 &#8211; y}\\\\{\\begin{array}{*{20}{l}}{2x + 2y = 4}\\end{array}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = &#8211; x + 3}\\\\{\\begin{array}{*{20}{l}}{y = &#8211; x + 2}\\end{array}}\\end{array}} \\right.}\\end{array}\\)<\/p>\n<p>O sistema \u00e9 imposs\u00edvel, pois as duas fun\u00e7\u00f5es afins possuem gr\u00e1ficos que s\u00e3o retas estritamente paralelas, visto que possuem declives iguais (\\( &#8211; 1\\)) e ordenadas na origem diferentes: \\(3\\) e \\(2\\).<\/p>\n<\/td>\n<td style=\"width: 50%;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25775\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25775\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5b.png\" data-orig-size=\"957,523\" 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_Pag197-5b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5b.png\" class=\"alignnone wp-image-25775\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5b-300x164.png\" alt=\"\" width=\"480\" height=\"262\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5b-300x164.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5b-768x420.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5b.png 957w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: left;\">\n<p>\\(\\begin{array}{*{20}{c}}{\\left\\{ {\\begin{array}{*{20}{l}}{x = 6 &#8211; y}\\\\{\\begin{array}{*{20}{l}}{\\frac{1}{2}x + \\frac{1}{2}y = 3}\\end{array}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = &#8211; x + 6}\\\\{\\begin{array}{*{20}{l}}{y = &#8211; x + 6}\\end{array}}\\end{array}} \\right.}\\end{array}\\)<\/p>\n<p>O sistema \u00e9 poss\u00edvel e indeterminado, pois as duas fun\u00e7\u00f5es afins possuem gr\u00e1ficos que s\u00e3o retas paralelas coincidentes, visto que possuem declives iguais (\\( &#8211; 1\\)) e ordenadas na origem iguais: \\(6\\).<\/p>\n<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25777\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25777\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5c.png\" data-orig-size=\"908,511\" 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_Pag197-5c\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5c.png\" class=\"alignnone wp-image-25777\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5c-300x169.png\" alt=\"\" width=\"480\" height=\"270\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5c-300x169.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5c-768x432.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5c.png 908w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25769' onClick='GTTabs_show(0,25769)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve graficamente os seguintes sistemas de equa\u00e7\u00f5es e classifica-os, justificando. \\(\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 7}\\\\{\\begin{array}{*{20}{l}}{x &#8211; y = 5}\\end{array}}\\end{array}} \\right.\\) \\(\\left\\{ {\\begin{array}{*{20}{l}}{x = 3 &#8211; y}\\\\{\\begin{array}{*{20}{l}}{2x + 2y = 4}\\end{array}}\\end{array}}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25776,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,239],"series":[],"class_list":["post-25769","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-sistema-de-equacoes"],"views":88,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag197-5b_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25769","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=25769"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25769\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25776"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25769"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25769"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25769"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25769"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}