{"id":26022,"date":"2023-05-24T19:51:01","date_gmt":"2023-05-24T18:51:01","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26022"},"modified":"2023-05-24T22:24:35","modified_gmt":"2023-05-24T21:24:35","slug":"a-rita-resolveu-graficamente-um-sistema","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26022","title":{"rendered":"A Rita resolveu graficamente um sistema"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26022' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26022' class='GTTabs_curr'><a  id=\"26022_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26022' ><a  id=\"26022_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_26022'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26023\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26023\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11.png\" data-orig-size=\"381,447\" 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_Pag204-11\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11.png\" class=\"alignright wp-image-26023\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11-256x300.png\" alt=\"\" width=\"300\" height=\"352\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11-256x300.png 256w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11.png 381w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>A Rita resolveu graficamente um sistema, como podes ver na figura.<\/p>\n<ol>\n<li>Indica a solu\u00e7\u00e3o do sistema de equa\u00e7\u00f5es que a Rita resolveu.<\/li>\n<li>Depois de teres encontrado as duas equa\u00e7\u00f5es do sistema, resolve-o, usando o m\u00e9todo de substitui\u00e7\u00e3o, de modo a confirmares a resposta dada na al\u00ednea anterior.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26022' onClick='GTTabs_show(1,26022)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26022'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26023\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26023\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11.png\" data-orig-size=\"381,447\" 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_Pag204-11\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11.png\" class=\"alignright wp-image-26023\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11-256x300.png\" alt=\"\" width=\"300\" height=\"352\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11-256x300.png 256w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11.png 381w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>A Rita resolveu graficamente um sistema, como podes ver na figura.<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>Indica a solu\u00e7\u00e3o do sistema de equa\u00e7\u00f5es que a Rita resolveu.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Depois de teres encontrado as duas equa\u00e7\u00f5es do sistema, resolve-o, usando o m\u00e9todo de substitui\u00e7\u00e3o, de modo a confirmares a resposta dada na al\u00ednea anterior.<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>A solu\u00e7\u00e3o do sistema de equa\u00e7\u00f5es que a Rita resolveu \u00e9 o par ordenado \\(\\left( {3, &#8211; \\frac{3}{2}} \\right)\\).<br \/><br \/><\/li>\n<li>Considerando que os pontos de coordenadas \\(\\left( {0,3} \\right)\\) e \\(\\left( {2,0} \\right)\\) pertencem a D<sub>1<\/sub> e que \\(\\left( {0, &#8211; \\frac{9}{2}} \\right)\\)\u00a0e \\(\\left( {\\frac{9}{2},0} \\right)\\) pertencem a D<sub>2<\/sub>, podemos determinar os declives dessas retas: \\({a_{{D_1}}} = \\frac{{3 &#8211; 0}}{{0 &#8211; 2}} = &#8211; \\frac{3}{2}\\) e \\({a_{{D_2}}} = \\frac{{ &#8211; \\frac{9}{2} &#8211; 0}}{{0 &#8211; \\frac{9}{2}}} = 1\\).<br \/>Assim, e tendo ainda em considera\u00e7\u00e3o as respetivas ordenadas na origem, as duas equa\u00e7\u00f5es do sistema s\u00e3o as indicadas a seguir: \\[\\left\\{ {\\begin{array}{*{20}{l}}{y = &#8211; \\frac{3}{2}x + 3}\\\\{y = x &#8211; \\frac{9}{2}}\\end{array}} \\right.\\] Resolvendo o sistema, vem: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{y = &#8211; \\frac{3}{2}x + 3}\\\\{y = x &#8211; \\frac{9}{2}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x &#8211; \\frac{9}{2} = &#8211; \\frac{3}{2}x + 3}\\\\{y = x &#8211; \\frac{9}{2}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{2x &#8211; 9 = &#8211; 3x + 6}\\\\{y = x &#8211; \\frac{9}{2}}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{5x = 15}\\\\{y = x &#8211; \\frac{9}{2}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = 3}\\\\{y = &#8211; \\frac{3}{2}}\\end{array}} \\right.}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{S = \\left\\{ {\\left( {3, &#8211; \\frac{3}{2}} \\right)} \\right\\}}&amp;{}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26022' onClick='GTTabs_show(0,26022)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A Rita resolveu graficamente um sistema, como podes ver na figura. Indica a solu\u00e7\u00e3o do sistema de equa\u00e7\u00f5es que a Rita resolveu. Depois de teres encontrado as duas equa\u00e7\u00f5es do sistema,&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":26024,"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-26022","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":85,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag204-11_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26022","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=26022"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26022\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26024"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26022"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26022"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26022"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}