{"id":26005,"date":"2023-05-24T09:40:34","date_gmt":"2023-05-24T08:40:34","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26005"},"modified":"2023-05-24T18:06:07","modified_gmt":"2023-05-24T17:06:07","slug":"resolve-os-seguintes-sistemas-de-equacoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26005","title":{"rendered":"Resolve os seguintes sistemas de equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26005' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26005' class='GTTabs_curr'><a  id=\"26005_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26005' ><a  id=\"26005_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_26005'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve os seguintes sistemas de equa\u00e7\u00f5es.<\/p>\n<ol>\n<li><br \/>\\(\\left\\{ {\\begin{array}{*{20}{l}}{2\\left( {x &#8211; 1} \\right) &#8211; 4y = 1}\\\\{3y = 2}\\end{array}} \\right.\\)<\/li>\n<li><br \/>\\(\\left\\{ {\\begin{array}{*{20}{l}}{2x + 3y = 10}\\\\{4x &#8211; y = &#8211; 1}\\end{array}} \\right.\\)<\/li>\n<li><br \/>\\(\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 7}\\\\{\\frac{{2x}}{5} = \\frac{{3y}}{7}}\\end{array}} \\right.\\)<\/li>\n<li><br \/>\\(\\left\\{ {\\begin{array}{*{20}{l}}{5\\left( {x + 1} \\right) + 3\\left( {y &#8211; 2} \\right) = 4}\\\\{8\\left( {x + 1} \\right) + 5\\left( {y &#8211; 2} \\right) = 9}\\end{array}} \\right.\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26005' onClick='GTTabs_show(1,26005)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26005'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{2\\left( {x &#8211; 1} \\right) &#8211; 4y = 1}\\\\{3y = 2}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{2x &#8211; 2 &#8211; 4y = 1}\\\\{y = \\frac{2}{3}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{2x &#8211; 2 &#8211; 4 \\times \\frac{2}{3} = 1}\\\\{y = \\frac{2}{3}}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{6x &#8211; 6 &#8211; 8 = 3}\\\\{y = \\frac{2}{3}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = \\frac{{17}}{6}}\\\\{y = \\frac{2}{3}}\\end{array}} \\right.}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{S = \\left\\{ {\\left( {\\frac{{17}}{6},\\frac{2}{3}} \\right)} \\right\\}}&amp;{}\\end{array}\\]<\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{2x + 3y = 10}\\\\{4x &#8211; y = &#8211; 1}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 4x + 1}\\\\{2x + 3\\left( {4x + 1} \\right) = 10}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{2x + 12x + 3 = 10}\\\\{y = 4x + 1}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{14x = 7}\\\\{y = 4x + 1}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = \\frac{1}{2}}\\\\{y = 3}\\end{array}} \\right.}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{S = \\left\\{ {\\left( {\\frac{1}{2},3} \\right)} \\right\\}}&amp;{}\\end{array}\\]<\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 7}\\\\{\\frac{{2x}}{5} = \\frac{{3y}}{7}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 7 &#8211; x}\\\\{14x = 15y}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{14x = 105 &#8211; 15x}\\\\{y = 7 &#8211; x}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = \\frac{{105}}{{29}}}\\\\{y = \\frac{{203}}{{29}} &#8211; \\frac{{105}}{{29}}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = \\frac{{105}}{{29}}}\\\\{y = \\frac{{98}}{{29}}}\\end{array}} \\right.}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{S = \\left\\{ {\\left( {\\frac{{105}}{{29}},\\frac{{98}}{{29}}} \\right)} \\right\\}}&amp;{}\\end{array}\\]<\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{5\\left( {x + 1} \\right) + 3\\left( {y &#8211; 2} \\right) = 4}\\\\{8\\left( {x + 1} \\right) + 5\\left( {y &#8211; 2} \\right) = 9}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{5x + 5 + 3y &#8211; 6 = 4}\\\\{8x + 8 + 5y &#8211; 10 = 9}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{5x + 3y = 5}\\\\{8x + 5y = 11}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = \\frac{{5 &#8211; 5x}}{3}}\\\\{8x + 5 \\times \\frac{{5 &#8211; 5x}}{3} = 11}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{8x + \\frac{{25}}{3} &#8211; \\frac{{25x}}{3} = 11}\\\\{y = \\frac{{5 &#8211; 5x}}{3}}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{ &#8211; \\frac{x}{3} = \\frac{8}{3}}\\\\{y = \\frac{{5 &#8211; 5x}}{3}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = &#8211; 8}\\\\{y = 15}\\end{array}} \\right.}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{S = \\left\\{ {\\left( { &#8211; 8,15} \\right)} \\right\\}}&amp;{}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26005' onClick='GTTabs_show(0,26005)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve os seguintes sistemas de equa\u00e7\u00f5es. \\(\\left\\{ {\\begin{array}{*{20}{l}}{2\\left( {x &#8211; 1} \\right) &#8211; 4y = 1}\\\\{3y = 2}\\end{array}} \\right.\\) \\(\\left\\{ {\\begin{array}{*{20}{l}}{2x + 3y = 10}\\\\{4x &#8211; y = &#8211; 1}\\end{array}} \\right.\\)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19189,"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-26005","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":76,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat75.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26005","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=26005"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26005\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19189"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26005"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}