{"id":643,"date":"2026-03-25T23:38:42","date_gmt":"2026-03-25T23:38:42","guid":{"rendered":"https:\/\/hackcuba.net\/?p=643"},"modified":"2026-03-25T23:38:43","modified_gmt":"2026-03-25T23:38:43","slug":"resolucion-de-sistemas-de-ecuaciones","status":"publish","type":"post","link":"https:\/\/hackcuba.net\/?p=643","title":{"rendered":"Resoluci\u00f3n de sistemas de ecuaciones"},"content":{"rendered":"\n<p>A cu\u00e1ntos de ustedes no les ha pasado que cuando estudian f\u00edsica o matem\u00e1tica, al acabar de resolver un problema en donde lo importante era el razonamiento, se encuentran con un sistema de tres ecuaciones con tres variables y, para colmo de males, con n\u00fameros decimales incluidos. <\/p>\n\n\n\n<!--more-->\n\n\n\n<p>A esa hora no tenemos otra forma de comprobar que resolvi\u00e9ndolo y comenzamos la tediosa tarea de calcular el sistema por cualquiera de los m\u00e9todos que conocemos. Pero despu\u00e9s de haber resuelto un problema duro de verdad esto no es tan sencillo.<\/p>\n\n\n\n<p>Para evitar estos conflictos aqu\u00ed va un c\u00f3digo escrito en Pascal que resuelve sistemas de tres con tres.<\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: delphi; title: ; notranslate\" title=\"\">\nvar\ni,j,k:integer;\nDet,Detx,Dety,Detz,ti1,ti2,ti3,x,y,z:real;\na,b,c:array&#x5B;1..3] of real;\nbegin\nfor i:=1 to 3 do\n  begin\n  write(&#039;a&#039;,i,&#039;:=&#039;);\n  readln(a&#x5B;i]);\n  end;\nfor j:=1 to 3 do\n  begin\n  write(&#039;b&#039;,j,&#039;:=&#039;);\n  readln(b&#x5B;j]);\n  end;\nfor k:=1 to 3 do\n  begin\n  write(&#039;c&#039;,k,&#039;:=&#039;);\n  readln(c&#x5B;k]);\n  end;\nwrite(&#039;t,rmino independiente1:=&#039;);\nreadln(ti1);\nwrite(&#039;t,rmino independiente2:=&#039;);\nreadln(ti2);\nwrite(&#039;t,rmino independiente3:=&#039;);\nreadln(ti3);\nDet:=a&#x5B;1]*b&#x5B;2]*c&#x5B;3]+a&#x5B;2]*b&#x5B;3]*c&#x5B;1]+a&#x5B;3]*b&#x5B;1]*c&#x5B;2]-a&#x5B;3]*b&#x5B;2]*c&#x5B;1]-a&#x5B;1]*b&#x5B;3]*c&#x5B;2]-a&#x5B;2]*b&#x5B;1]*c&#x5B;3];\nIf Det=0 Then writeln(&#039;el sistema no tiene soluci\u00f3n&#039;)\nElse\n  Begin\n  Detx:=ti1*b&#x5B;2]*c&#x5B;3]+ti2*b&#x5B;3]*c&#x5B;1]+ti3*b&#x5B;1]*c&#x5B;2]-ti3*b&#x5B;2]*c&#x5B;1]-ti1*b&#x5B;3]*c&#x5B;2]-ti2*b&#x5B;1]*c&#x5B;3];\n  Dety:=a&#x5B;1]*ti2*c&#x5B;3]+a&#x5B;2]*ti3*c&#x5B;1]+a&#x5B;3]*ti1*c&#x5B;2]-a&#x5B;3]*ti2*c&#x5B;1]-a&#x5B;1]*ti3*c&#x5B;2]-a&#x5B;2]*ti1*c&#x5B;3];\n  Detz:=a&#x5B;1]*b&#x5B;2]*ti3+a&#x5B;2]*b&#x5B;3]*ti1+a&#x5B;3]*b&#x5B;1]*ti2-a&#x5B;3]*b&#x5B;2]*ti1-a&#x5B;1]*b&#x5B;3]*ti2-a&#x5B;2]*b&#x5B;1]*ti3;\n  x:=Detx\/Det;\n  y:=Dety\/Det;\n  z:=Detz\/Det;\n  Writeln(&#039;x:=&#039;,x:5:2);\n  Writeln(&#039;y:=&#039;,y:5:2);\n  Writeln(&#039;z:=&#039;,z:5:2);\n  end;\nend.\n<\/pre><\/div>\n\n\n<h2 class=\"wp-block-heading\">Para saber m\u00e1s&#8230;<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"http:\/\/pascal-central.com\/ppl\/index.html\" target=\"_blank\" rel=\"noreferrer noopener\">The Pascal Programming Language<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/writerguy.users.btopenworld.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Free online Pascal book<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/es.wikipedia.org\/wiki\/Sistema_de_ecuaciones\" target=\"_blank\" rel=\"noreferrer noopener\">Wikipedia::Sistemas de ecuaciones<\/a><\/li>\n<\/ul>\n\n\n\n<p>Escrito por Gandalf [<a href=\"mailto:yoslaine.fernandez@infomed.sld.cu\">yoslaine.fernandez@infomed.sld.cu<\/a>]<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A cu\u00e1ntos de ustedes no les ha pasado que cuando estudian f\u00edsica o matem\u00e1tica, al acabar de resolver<\/p>\n","protected":false},"author":2,"featured_media":510,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[59,36],"tags":[88,89,140,38],"class_list":["post-643","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-codigos","category-proyecto-blackhat","tag-codigos","tag-pascal","tag-problemas-matematicos","tag-proyecto-blackhat"],"_links":{"self":[{"href":"https:\/\/hackcuba.net\/index.php?rest_route=\/wp\/v2\/posts\/643","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hackcuba.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hackcuba.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hackcuba.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/hackcuba.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=643"}],"version-history":[{"count":1,"href":"https:\/\/hackcuba.net\/index.php?rest_route=\/wp\/v2\/posts\/643\/revisions"}],"predecessor-version":[{"id":644,"href":"https:\/\/hackcuba.net\/index.php?rest_route=\/wp\/v2\/posts\/643\/revisions\/644"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hackcuba.net\/index.php?rest_route=\/wp\/v2\/media\/510"}],"wp:attachment":[{"href":"https:\/\/hackcuba.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hackcuba.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hackcuba.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}