{"id":26202,"date":"2023-06-04T23:34:17","date_gmt":"2023-06-04T22:34:17","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26202"},"modified":"2023-06-04T23:43:59","modified_gmt":"2023-06-04T22:43:59","slug":"mais-um-sistema-de-equacoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26202","title":{"rendered":"Mais um sistema de equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26202' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26202' class='GTTabs_curr'><a  id=\"26202_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26202' ><a  id=\"26202_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_26202'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A solu\u00e7\u00e3o do sistema de equa\u00e7\u00f5es \\[\\left\\{ {\\begin{array}{*{20}{l}}{2x &#8211; y = &#8211; 1}\\\\{y &#8211; 3x = &#8211; 1}\\end{array}} \\right.\\] \u00e9 o par ordenado \\(\\left( {x,y} \\right)\\).<\/p>\n<p>O valor de \\(xy\\) \u00e9:<\/p>\n<p><strong>[A]<\/strong> \u221210\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> 10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> 4<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26202' onClick='GTTabs_show(1,26202)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26202'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A solu\u00e7\u00e3o do sistema de equa\u00e7\u00f5es \\[\\left\\{ {\\begin{array}{*{20}{l}}{2x &#8211; y = &#8211; 1}\\\\{y &#8211; 3x = &#8211; 1}\\end{array}} \\right.\\] \u00e9 o par ordenado \\(\\left( {x,y} \\right)\\).<\/p>\n<p>O valor de \\(xy\\) \u00e9:<\/p>\n<p><strong>[A]<\/strong> \u221210\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> 10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> 4<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>Resolvendo o sistema de equa\u00e7\u00f5es, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{2x &#8211; y = &#8211; 1}\\\\{y &#8211; 3x = &#8211; 1}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 3x &#8211; 1}\\\\{2x &#8211; \\left( {3x &#8211; 1} \\right) = &#8211; 1}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 3x &#8211; 1}\\\\{ &#8211; x + 1 = &#8211; 1}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = 2}\\\\{y = 5}\\end{array}} \\right.}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>Logo, \\(xy = 2 \\times 5 = 10\\).<\/p>\n<p>Portanto, a op\u00e7\u00e3o correta \u00e9 <strong>[B]<\/strong> 10.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26202' onClick='GTTabs_show(0,26202)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A solu\u00e7\u00e3o do sistema de equa\u00e7\u00f5es \\[\\left\\{ {\\begin{array}{*{20}{l}}{2x &#8211; y = &#8211; 1}\\\\{y &#8211; 3x = &#8211; 1}\\end{array}} \\right.\\] \u00e9 o par ordenado \\(\\left( {x,y} \\right)\\). O valor de \\(xy\\) \u00e9:&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19269,"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-26202","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":66,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat90.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26202","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=26202"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26202\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19269"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26202"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26202"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26202"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}