{"id":1268,"date":"2025-09-16T21:01:22","date_gmt":"2025-09-17T03:01:22","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=1268"},"modified":"2025-09-16T21:32:43","modified_gmt":"2025-09-17T03:32:43","slug":"temporary-title-790-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=1268","title":{"rendered":"Sistema de ecuaciones con tres inc\u00f3gnitas"},"content":{"rendered":"<div id=\"cmsmasters_row_\" class=\"cmsmasters_row cmsmasters_color_scheme_default cmsmasters_row_top_default cmsmasters_row_bot_default cmsmasters_row_boxed\">\n<div class=\"cmsmasters_row_outer_parent\">\n<div class=\"cmsmasters_row_outer\">\n<div class=\"cmsmasters_row_inner\">\n<div class=\"cmsmasters_row_margin\">\n<div id=\"cmsmasters_column_\" class=\"cmsmasters_column one_first\">\n<div class=\"cmsmasters_column_inner\"><div class=\"cmsmasters_text\" data-animation=\"fadeIn\">\n<p data-start=\"2136\" data-end=\"2382\">Un <strong data-start=\"2139\" data-end=\"2184\">sistema de ecuaciones con tres inc\u00f3gnitas<\/strong> es un conjunto de tres ecuaciones lineales que se deben resolver de manera simult\u00e1nea. El objetivo es encontrar el valor de las tres variables que satisfacen todas las ecuaciones al mismo tiempo.<\/p>\n<p data-start=\"2384\" data-end=\"2470\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3a5.svg\" alt=\"\ud83c\udfa5\" \/> <strong data-start=\"2387\" data-end=\"2409\">Mira el video aqu\u00ed<\/strong><\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/FwHaH4dJrU8?si=jgDIydjdaFikuriP\" width=\"1120\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2472\" data-end=\"2475\" \/>\n<h2 data-start=\"2477\" data-end=\"2523\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4cd.svg\" alt=\"\ud83d\udccd\" \/> \u00bfQu\u00e9 es un sistema de tres inc\u00f3gnitas?<\/h2>\n<p data-start=\"2524\" data-end=\"2754\">Un sistema con tres variables, generalmente representadas como <span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span>, <span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span> y <span class=\"katex\"><span class=\"katex-mathml\">zz<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">z<\/span><\/span><\/span><\/span>, permite analizar problemas m\u00e1s complejos que los de dos inc\u00f3gnitas. Se usan cuando hay varias condiciones que se deben cumplir al mismo tiempo.<\/p>\n<p data-start=\"2756\" data-end=\"2775\">Ejemplo sencillo:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">x+y+z=6<\/span><\/span><\/span><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">2x\u2212y+z=3<\/span><\/span><\/span> <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u00a0<\/span><\/span><\/span><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">z<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span><\/p>\n<hr data-start=\"2851\" data-end=\"2854\" \/>\n<h2 data-start=\"2856\" data-end=\"2886\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f6e0.svg\" alt=\"\ud83d\udee0\ufe0f\" \/> M\u00e9todos de resoluci\u00f3n<\/h2>\n<p data-start=\"2887\" data-end=\"2941\">Existen varios m\u00e9todos para resolver estos sistemas:<\/p>\n<ol>\n<li data-start=\"2945\" data-end=\"3031\"><strong data-start=\"2945\" data-end=\"2961\">Sustituci\u00f3n:<\/strong> resolver una ecuaci\u00f3n para una variable y sustituirla en las dem\u00e1s.<\/li>\n<li data-start=\"3035\" data-end=\"3101\"><strong data-start=\"3035\" data-end=\"3050\">Igualaci\u00f3n:<\/strong> igualar expresiones para simplificar el sistema.<\/li>\n<li data-start=\"3105\" data-end=\"3167\"><strong data-start=\"3105\" data-end=\"3119\">Reducci\u00f3n:<\/strong> combinar ecuaciones para eliminar inc\u00f3gnitas.<\/li>\n<li data-start=\"3171\" data-end=\"3246\"><strong data-start=\"3171\" data-end=\"3198\">Matriz o determinantes:<\/strong> usar el m\u00e9todo de Gauss o la regla de Cramer.<\/li>\n<\/ol>\n<hr data-start=\"3248\" data-end=\"3251\" \/>\n<h2 data-start=\"3253\" data-end=\"3289\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f30d.svg\" alt=\"\ud83c\udf0d\" \/> Aplicaciones en la vida real<\/h2>\n<ul>\n<li data-start=\"3292\" data-end=\"3344\"><strong data-start=\"3292\" data-end=\"3307\">Ingenier\u00eda:<\/strong> calcular fuerzas en equilibrio. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2699.svg\" alt=\"\u2699\ufe0f\" \/><\/li>\n<li data-start=\"3347\" data-end=\"3423\"><strong data-start=\"3347\" data-end=\"3360\">Econom\u00eda:<\/strong> analizar el balance entre producci\u00f3n, costos y ganancias. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4b0.svg\" alt=\"\ud83d\udcb0\" \/><\/li>\n<li data-start=\"3426\" data-end=\"3497\"><strong data-start=\"3426\" data-end=\"3438\">Qu\u00edmica:<\/strong> resolver mezclas y reacciones con varias condiciones. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2697.svg\" alt=\"\u2697\ufe0f\" \/><\/li>\n<li data-start=\"3500\" data-end=\"3565\"><strong data-start=\"3500\" data-end=\"3519\">Administraci\u00f3n:<\/strong> asignar recursos entre diferentes \u00e1reas. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4ca.svg\" alt=\"\ud83d\udcca\" \/><\/li>\n<\/ul>\n<hr data-start=\"3567\" data-end=\"3570\" \/>\n<h2 data-start=\"3572\" data-end=\"3599\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f393.svg\" alt=\"\ud83c\udf93\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"3600\" data-end=\"3821\">El <strong data-start=\"3603\" data-end=\"3658\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala ofrece herramientas claras para que j\u00f3venes y adultos comprendan y apliquen estos temas en su vida acad\u00e9mica y laboral.<\/p>\n<hr data-start=\"3823\" data-end=\"3826\" \/>\n<h2 data-start=\"3828\" data-end=\"3845\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2705.svg\" alt=\"\u2705\" \/> Conclusi\u00f3n<\/h2>\n<p data-start=\"3846\" data-end=\"3997\">Resolver un <strong data-start=\"3858\" data-end=\"3903\">sistema de ecuaciones con tres inc\u00f3gnitas<\/strong> desarrolla el pensamiento l\u00f3gico y fortalece la capacidad de enfrentar problemas complejos.<\/p>\n<p data-start=\"3999\" data-end=\"4085\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f449.svg\" alt=\"\ud83d\udc49\" \/> Con el <strong data-start=\"4009\" data-end=\"4019\">PRONEA<\/strong>, aprender matem\u00e1ticas es posible en cualquier etapa de la vida.<\/p>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":1270,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":""},"categories":[33,39],"tags":[],"class_list":["post-1268","post","type-post","status-publish","format-image","has-post-thumbnail","hentry","category-matematicas","category-recursos","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1268","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1268"}],"version-history":[{"count":4,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1268\/revisions"}],"predecessor-version":[{"id":1275,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1268\/revisions\/1275"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/1270"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1268"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}