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{"id":25944,"date":"2023-05-22T21:55:34","date_gmt":"2023-05-22T20:55:34","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25944"},"modified":"2023-05-22T22:33:14","modified_gmt":"2023-05-22T21:33:14","slug":"considera-a-equacao-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25944","title":{"rendered":"Considera a equa\u00e7\u00e3o"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25944' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25944' class='GTTabs_curr'><a  id=\"25944_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25944' ><a  id=\"25944_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_25944'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera a equa\u00e7\u00e3o: \\(\\frac{3}{2}x + 2y = 3\\)<\/p>\n<ol>\n<li>O par \\(\\left( {2, &#8211; 1} \\right)\\) \u00e9 solu\u00e7\u00e3o?<\/li>\n<li>Resolve a equa\u00e7\u00e3o em ordem a <em>y<\/em>.<\/li>\n<li>Procura o valor de <em>y<\/em> para \\(x = &#8211; 4\\).<\/li>\n<li>Qual \u00e9 o valor de <em>x<\/em> para \\(y = 0\\)?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25944' onClick='GTTabs_show(1,25944)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25944'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Considera a equa\u00e7\u00e3o: \\[\\frac{3}{2}x + 2y = 3\\]<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<ol>\n<li>Na equa\u00e7\u00e3o dada, substituindo <em>x<\/em> por 2 e <em>y<\/em> por \u22121, obtemos uma proposi\u00e7\u00e3o falsa: \\[\\begin{array}{*{20}{c}}{\\frac{3}{2} \\times 2 + 2 \\times \\left( { &#8211; 1} \\right) = 3}&amp; \\Leftrightarrow &amp;{1 = 3}\\end{array}\\] Logo, o par \\(\\left( {2, &#8211; 1} \\right)\\) n\u00e3o \u00e9 solu\u00e7\u00e3o da equa\u00e7\u00e3o.<br \/><br \/><\/li>\n<li>Resolvendo a equa\u00e7\u00e3o em ordem a <em>y<\/em>, temos:<br \/>\\[\\begin{array}{*{20}{l}}{\\frac{3}{2}x + 2y = 3}&amp; \\Leftrightarrow &amp;{3x + 4y = 6}\\\\{}&amp; \\Leftrightarrow &amp;{4y = 6 &#8211; 3x}\\\\{}&amp; \\Leftrightarrow &amp;{y = &#8211; \\frac{3}{4}x + \\frac{3}{2}}\\end{array}\\]<\/li>\n<li>Procurando o valor de <em>y<\/em> para \\(x = &#8211; 4\\), temos: \\[y = &#8211; \\frac{3}{4} \\times \\left( { &#8211; 4} \\right) + \\frac{3}{2} = 3 + \\frac{3}{2} = \\frac{9}{2}\\]<\/li>\n<li>O valor de <em>x<\/em> para \\(y = 0\\) \u00e9:<br \/>\\[\\begin{array}{*{20}{l}}{\\frac{3}{2}x + 2 \\times 0 = 3}&amp; \\Leftrightarrow &amp;{3x + 0 = 6}\\\\{}&amp; \\Leftrightarrow &amp;{x = 2}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25944' onClick='GTTabs_show(0,25944)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a equa\u00e7\u00e3o: \\(\\frac{3}{2}x + 2y = 3\\) O par \\(\\left( {2, &#8211; 1} \\right)\\) \u00e9 solu\u00e7\u00e3o? Resolve a equa\u00e7\u00e3o em ordem a y. 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