{"id":27722,"date":"2025-06-20T06:11:22","date_gmt":"2025-06-20T06:11:22","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27722"},"modified":"2025-06-20T06:11:23","modified_gmt":"2025-06-20T06:11:23","slug":"finish-solving-the-system-of-equations-x-5y-6-and-x-2y-3","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/finish-solving-the-system-of-equations-x-5y-6-and-x-2y-3\/","title":{"rendered":"Finish solving the system of equations X &#8211; 5y = 6 and -x + 2y = -3."},"content":{"rendered":"\n<p>Finish solving the system of equations X &#8211; 5y = 6 and -x + 2y = -3. What is the value of y? Substitute the value of y back into one of the original equations to find the value of x. What is the value of x?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given a system of equations:<\/p>\n\n\n\n<p>1)\u2003x &#8211; 5y = 6<br>2)\u2003-x + 2y = -3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Add the two equations<\/h3>\n\n\n\n<p>We observe that if we add both equations together, the <strong>x<\/strong> terms will cancel out:(x\u22125y)+(\u2212x+2y)=6+(\u22123)(x &#8211; 5y) + (-x + 2y) = 6 + (-3)(x\u22125y)+(\u2212x+2y)=6+(\u22123)<\/p>\n\n\n\n<p>Simplify:x\u22125y\u2212x+2y=3x &#8211; 5y &#8211; x + 2y = 3x\u22125y\u2212x+2y=3\u22123y=3-3y = 3\u22123y=3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve for <strong>y<\/strong><\/h3>\n\n\n\n<p>Divide both sides by -3:y=\u22121y = -1y=\u22121<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Substitute y = -1 into one of the original equations<\/h3>\n\n\n\n<p>We will use the first equation:x\u22125y=6x &#8211; 5y = 6x\u22125y=6<\/p>\n\n\n\n<p>Substitute <strong>y = -1<\/strong>:x\u22125(\u22121)=6x &#8211; 5(-1) = 6x\u22125(\u22121)=6x+5=6x + 5 = 6x+5=6x=1x = 1x=1<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>y = -1<\/strong><\/li>\n\n\n\n<li><strong>x = 1<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation <\/h3>\n\n\n\n<p>To solve a system of linear equations, one effective method is the elimination method, which involves combining the equations to eliminate one variable. In the given system:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x &#8211; 5y = 6<\/li>\n\n\n\n<li>-x + 2y = -3<\/li>\n<\/ul>\n\n\n\n<p>We notice that the coefficients of <strong>x<\/strong> are opposites (x and -x). This makes it easy to eliminate <strong>x<\/strong> by adding the two equations. Doing this step-by-step:<\/p>\n\n\n\n<p>(x &#8211; 5y) + (-x + 2y) results in -3y on the left side and 3 on the right side, so we get the equation:<\/p>\n\n\n\n<p>-3y = 3.<\/p>\n\n\n\n<p>Dividing both sides by -3 gives y = -1.<\/p>\n\n\n\n<p>Once we have the value of y, we can substitute it back into either of the original equations to find the corresponding value of x. Using the first equation:<\/p>\n\n\n\n<p>x &#8211; 5y = 6 becomes x &#8211; 5(-1) = 6. This simplifies to x + 5 = 6, and solving for x gives x = 1.<\/p>\n\n\n\n<p>This process confirms the solution is the ordered pair (1, -1). If you plug these values into the second original equation:<\/p>\n\n\n\n<p>-x + 2y = -3 becomes -1 + 2(-1) = -3, which is true.<\/p>\n\n\n\n<p>Thus, both x and y satisfy the system. The solution is correct.<\/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-banner8-173.jpeg\" alt=\"\" class=\"wp-image-27723\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-173.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-173-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-173-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Finish solving the system of equations X &#8211; 5y = 6 and -x + 2y = -3. What is the value of y? Substitute the value of y back into one of the original equations to find the value of x. What is the value of x? The Correct Answer and Explanation is: We are [&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-27722","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27722","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=27722"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27722\/revisions"}],"predecessor-version":[{"id":27724,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27722\/revisions\/27724"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27722"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27722"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27722"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}