{"id":33050,"date":"2025-06-23T05:44:01","date_gmt":"2025-06-23T05:44:01","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=33050"},"modified":"2025-06-23T05:44:02","modified_gmt":"2025-06-23T05:44:02","slug":"6x-4y-6-6x-2y-12","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/6x-4y-6-6x-2y-12\/","title":{"rendered":"6x + 4y = 6, 6x + 2y = 12"},"content":{"rendered":"\n<p>6x + 4y = 6, 6x + 2y = 12<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p>We are to solve the system of equations:<\/p>\n\n\n\n<p><strong>1)<\/strong> 6x+4y=66x + 4y = 66x+4y=6<br><strong>2)<\/strong> 6x+2y=126x + 2y = 126x+2y=12<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1: Eliminate one variable using the elimination method<\/h4>\n\n\n\n<p>Subtract equation 2 from equation 1:(6x+4y)\u2212(6x+2y)=6\u221212(6x + 4y) &#8211; (6x + 2y) = 6 &#8211; 12(6x+4y)\u2212(6x+2y)=6\u221212<\/p>\n\n\n\n<p>Simplifying:6x\u22126x+4y\u22122y=\u221266x &#8211; 6x + 4y &#8211; 2y = -66x\u22126x+4y\u22122y=\u221262y=\u221262y = -62y=\u22126<\/p>\n\n\n\n<p>Divide both sides by 2:y=\u22123y = -3y=\u22123<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 2: Substitute the value of yyy into one of the original equations<\/h4>\n\n\n\n<p>We use equation 2:6x+2y=126x + 2y = 126x+2y=12<\/p>\n\n\n\n<p>Substitute y=\u22123y = -3y=\u22123:6x+2(\u22123)=126x + 2(-3) = 126x+2(\u22123)=12<\/p>\n\n\n\n<p>Simplifying:6x\u22126=126x &#8211; 6 = 126x\u22126=12<\/p>\n\n\n\n<p>Add 6 to both sides:6x=186x = 186x=18<\/p>\n\n\n\n<p>Divide both sides by 6:x=3x = 3x=3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Solution:<\/h3>\n\n\n\n<p>x=3,y=\u22123x = 3, \\quad y = -3x=3,y=\u22123<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>To solve this system of linear equations, we use the elimination method, which involves eliminating one variable to simplify the system into a single-variable equation. We are given two linear equations involving xxx and yyy:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>6x+4y=66x + 4y = 66x+4y=6<\/li>\n\n\n\n<li>6x+2y=126x + 2y = 126x+2y=12<\/li>\n<\/ol>\n\n\n\n<p>The first step is to eliminate xxx by subtracting equation 2 from equation 1. The xxx terms 6x6x6x cancel each other out, leaving us with:4y\u22122y=6\u2212124y &#8211; 2y = 6 &#8211; 124y\u22122y=6\u221212<\/p>\n\n\n\n<p>This simplifies to 2y=\u221262y = -62y=\u22126. Solving for yyy gives y=\u22123y = -3y=\u22123.<\/p>\n\n\n\n<p>Once we have the value of yyy, we substitute it back into one of the original equations to find xxx. Using the second equation:6x+2y=126x + 2y = 126x+2y=12<\/p>\n\n\n\n<p>Replacing yyy with \u22123-3\u22123:6x+2(\u22123)=126x + 2(-3) = 126x+2(\u22123)=12<\/p>\n\n\n\n<p>This simplifies to:6x\u22126=126x &#8211; 6 = 126x\u22126=12<\/p>\n\n\n\n<p>Adding 6 to both sides:6x=186x = 186x=18<\/p>\n\n\n\n<p>Dividing both sides by 6:x=3x = 3x=3<\/p>\n\n\n\n<p>Thus, the solution to the system is x=3x = 3x=3 and y=\u22123y = -3y=\u22123.<\/p>\n\n\n\n<p>We can verify by substituting these values into both original equations to confirm they satisfy both, ensuring the solution is correct. This method is reliable for solving linear systems.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-483.jpeg\" alt=\"\" class=\"wp-image-33051\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-483.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-483-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-483-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>6x + 4y = 6, 6x + 2y = 12 The Correct Answer and Explanation is: Correct Answer: We are to solve the system of equations: 1) 6x+4y=66x + 4y = 66x+4y=62) 6x+2y=126x + 2y = 126x+2y=12 Step 1: Eliminate one variable using the elimination method Subtract equation 2 from equation 1:(6x+4y)\u2212(6x+2y)=6\u221212(6x + 4y) &#8211; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-33050","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33050","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=33050"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33050\/revisions"}],"predecessor-version":[{"id":33052,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33050\/revisions\/33052"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}