{"id":1318,"date":"2025-10-10T18:11:20","date_gmt":"2025-10-11T00:11:20","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=1318"},"modified":"2025-10-10T18:13:32","modified_gmt":"2025-10-11T00:13:32","slug":"temporary-title-790-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=1318","title":{"rendered":"Problemas con sistemas de ecuaciones"},"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=\"2636\" data-end=\"2845\">Resolver <strong data-start=\"2645\" data-end=\"2685\">problemas con sistemas de ecuaciones<\/strong> es una de las aplicaciones m\u00e1s \u00fatiles del \u00e1lgebra, ya que permite representar situaciones reales con expresiones matem\u00e1ticas y encontrar soluciones precisas.<\/p>\n<p data-start=\"2847\" data-end=\"2963\"><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=\"2850\" data-end=\"2884\">Mira aqu\u00ed el video del tema<\/strong>,<\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/bLQguDuLvis?si=RPh_PTfVJl63EsuH\" width=\"1120\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2965\" data-end=\"2968\" \/>\n<h2 data-start=\"2970\" data-end=\"3011\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f50e.svg\" alt=\"\ud83d\udd0e\" \/> \u00bfQu\u00e9 es un sistema de ecuaciones?<\/h2>\n<p data-start=\"3012\" data-end=\"3222\">Un <strong data-start=\"3015\" data-end=\"3040\">sistema de ecuaciones<\/strong> es un conjunto de dos o m\u00e1s ecuaciones que tienen variables en com\u00fan.<br data-start=\"3110\" data-end=\"3113\" \/>El objetivo es encontrar los valores de esas variables que satisfacen todas las ecuaciones al mismo tiempo.<\/p>\n<p data-start=\"3224\" data-end=\"3238\">Por ejemplo:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"minner\"><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1320\" src=\"https:\/\/portal.pronea.gt\/wp-content\/uploads\/2025\/10\/sis_ecuacion1.png\" alt=\"sistema de ecuaci\u00f3n\" width=\"191\" height=\"114\" \/><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"3298\" data-end=\"3408\">Resolver este sistema significa encontrar los valores de <strong data-start=\"3355\" data-end=\"3360\">x<\/strong> y <strong data-start=\"3363\" data-end=\"3368\">y<\/strong> que hacen verdadera ambas ecuaciones.<\/p>\n<hr data-start=\"3410\" data-end=\"3413\" \/>\n<h2 data-start=\"3415\" data-end=\"3467\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f9e9.svg\" alt=\"\ud83e\udde9\" \/> M\u00e9todos para resolver sistemas de ecuaciones<\/h2>\n<p data-start=\"3468\" data-end=\"3511\">Existen diferentes formas de resolverlos:<\/p>\n<ul>\n<li data-start=\"3514\" data-end=\"3602\"><strong data-start=\"3514\" data-end=\"3540\">M\u00e9todo de sustituci\u00f3n:<\/strong> se despeja una variable y se sustituye en la otra ecuaci\u00f3n.<\/li>\n<li data-start=\"3605\" data-end=\"3682\"><strong data-start=\"3605\" data-end=\"3630\">M\u00e9todo de igualaci\u00f3n:<\/strong> se igualan las expresiones de una misma variable.<\/li>\n<li data-start=\"3685\" data-end=\"3768\"><strong data-start=\"3685\" data-end=\"3709\">M\u00e9todo de reducci\u00f3n:<\/strong> se suman o restan ecuaciones para eliminar una variable.<\/li>\n<\/ul>\n<p data-start=\"3770\" data-end=\"3852\">Cada m\u00e9todo tiene su utilidad, dependiendo del tipo de problema que se enfrente.<\/p>\n<hr data-start=\"3854\" data-end=\"3857\" \/>\n<h2 data-start=\"3859\" data-end=\"3895\"><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\" \/> Aplicaciones en la vida real<\/h2>\n<p data-start=\"3896\" data-end=\"3958\">Los sistemas de ecuaciones permiten resolver problemas como:<\/p>\n<ul>\n<li data-start=\"3961\" data-end=\"4007\">Calcular precios de productos en conjunto <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=\"4010\" data-end=\"4055\">Analizar mezclas o proporciones qu\u00edmicas <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=\"4058\" data-end=\"4092\">Determinar rutas o distancias <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f697.svg\" alt=\"\ud83d\ude97\" \/><\/li>\n<li data-start=\"4095\" data-end=\"4122\">Balancear presupuestos <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4c8.svg\" alt=\"\ud83d\udcc8\" \/><\/li>\n<\/ul>\n<p data-start=\"4124\" data-end=\"4227\">En todos estos casos, las ecuaciones nos ayudan a traducir una situaci\u00f3n real al lenguaje matem\u00e1tico.<\/p>\n<hr data-start=\"4229\" data-end=\"4232\" \/>\n<h2 data-start=\"4234\" data-end=\"4258\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f9ee.svg\" alt=\"\ud83e\uddee\" \/> Ejemplo pr\u00e1ctico<\/h2>\n<p data-start=\"4259\" data-end=\"4376\"><strong data-start=\"4259\" data-end=\"4272\">Problema:<\/strong><br data-start=\"4272\" data-end=\"4275\" \/>En una feria, dos personas compraron diferentes combinaciones de entradas y bebidas.<br data-start=\"4359\" data-end=\"4362\" \/>Sabemos que:<\/p>\n<ul>\n<li data-start=\"4379\" data-end=\"4415\">2 entradas y 1 bebida cuestan Q25.<\/li>\n<li data-start=\"4418\" data-end=\"4454\">1 entrada y 2 bebidas cuestan Q20.<\/li>\n<\/ul>\n<p data-start=\"4456\" data-end=\"4515\">Para saber cu\u00e1nto cuesta cada producto, podemos plantear:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"minner\"><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1321\" src=\"https:\/\/portal.pronea.gt\/wp-content\/uploads\/2025\/10\/sis_ecuacion2.png\" alt=\"Sistema de ecuaci\u00f3n\" width=\"194\" height=\"114\" \/><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"4577\" data-end=\"4680\">Resolviendo el sistema, encontramos que:<br data-start=\"4617\" data-end=\"4620\" \/><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f39f.svg\" alt=\"\ud83c\udf9f\ufe0f\" \/> La entrada cuesta <strong data-start=\"4642\" data-end=\"4649\">Q10<\/strong><br data-start=\"4649\" data-end=\"4652\" \/><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f964.svg\" alt=\"\ud83e\udd64\" \/> La bebida cuesta <strong data-start=\"4672\" data-end=\"4678\">Q5<\/strong><\/p>\n<p data-start=\"4682\" data-end=\"4736\">\u00a1As\u00ed de \u00fatil puede ser el \u00e1lgebra en tu vida diaria!<\/p>\n<hr data-start=\"4738\" data-end=\"4741\" \/>\n<h2 data-start=\"4743\" data-end=\"4770\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f31f.svg\" alt=\"\ud83c\udf1f\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"4771\" data-end=\"4973\">El <strong data-start=\"4774\" data-end=\"4829\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala brinda oportunidades de aprendizaje flexible para j\u00f3venes y adultos que desean retomar sus estudios.<\/p>\n<p data-start=\"4975\" data-end=\"5143\">Con materiales claros, ejemplos pr\u00e1cticos y acompa\u00f1amiento pedag\u00f3gico, cada video te ayuda a fortalecer tu razonamiento l\u00f3gico y tu confianza para resolver problemas.<\/p>\n<hr data-start=\"5145\" data-end=\"5148\" \/>\n<h2 data-start=\"5150\" data-end=\"5167\"><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=\"5168\" data-end=\"5399\">Los <strong data-start=\"5172\" data-end=\"5212\">problemas con sistemas de ecuaciones<\/strong> no solo ense\u00f1an a calcular, sino a <strong data-start=\"5248\" data-end=\"5280\">razonar, analizar y resolver<\/strong>.<br data-start=\"5281\" data-end=\"5284\" \/>Con <strong data-start=\"5288\" data-end=\"5298\">PRONEA<\/strong>, las matem\u00e1ticas se convierten en una herramienta \u00fatil para tu vida personal, laboral y acad\u00e9mica.<\/p>\n<p data-start=\"5401\" data-end=\"5449\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4d8.svg\" alt=\"\ud83d\udcd8\" \/> \u00a1Aprende, analiza y resuelve con confianza!<\/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":1323,"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-1318","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\/1318","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=1318"}],"version-history":[{"count":2,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1318\/revisions"}],"predecessor-version":[{"id":1322,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1318\/revisions\/1322"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/1323"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1318"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}