{"id":262863,"date":"2025-07-20T20:08:07","date_gmt":"2025-07-20T20:08:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=262863"},"modified":"2025-07-20T20:08:09","modified_gmt":"2025-07-20T20:08:09","slug":"for-the-equation-if-7x-8y-25-and-8x-7y-35-and-then-x-y","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/20\/for-the-equation-if-7x-8y-25-and-8x-7y-35-and-then-x-y\/","title":{"rendered":"For the equation if 7x + 8y = 25 and 8x + 7y = 35 and then x + y."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-602.png\" alt=\"\" class=\"wp-image-262864\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is&nbsp;<strong>4<\/strong>.<\/p>\n\n\n\n<p>This problem provides a system of two linear equations and asks for the value of the sum&nbsp;x + y. The given equations are:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>7x + 8y = 25<\/li>\n\n\n\n<li>8x + 7y = 35<\/li>\n<\/ol>\n\n\n\n<p>While you could solve for the individual values of&nbsp;x&nbsp;and&nbsp;y&nbsp;using methods like substitution or elimination, there is a more direct and efficient strategy for this specific type of problem. The key is to observe the structure of the equations. Notice that the coefficients of the&nbsp;x&nbsp;and&nbsp;y&nbsp;variables are swapped between the two equations. In the first equation, the coefficient of&nbsp;x&nbsp;is 7 and&nbsp;y&nbsp;is 8; in the second, the coefficient of&nbsp;x&nbsp;is 8 and&nbsp;y&nbsp;is 7.<\/p>\n\n\n\n<p>This symmetrical pattern is a strong hint that adding the two equations together will simplify the problem significantly. Let&#8217;s perform this addition:<br>(7x + 8y) + (8x + 7y) = 25 + 35<\/p>\n\n\n\n<p>Next, we can group the like terms on the left side of the equation:<br>(7x + 8x) + (8y + 7y) = 60<\/p>\n\n\n\n<p>Combining these terms gives us a much simpler equation:<br>15x + 15y = 60<\/p>\n\n\n\n<p>Now, you can see that both terms on the left side share a common factor of 15. We can factor this common coefficient out:<br>15(x + y) = 60<\/p>\n\n\n\n<p>The problem asks for the value of&nbsp;x + y, which is exactly the expression we have inside the parentheses. To isolate this expression, we simply need to divide both sides of the equation by 15:<br>x + y = 60 \/ 15<br>x + y = 4<\/p>\n\n\n\n<p>This method allows us to find the value of&nbsp;x + y&nbsp;without ever needing to calculate&nbsp;x&nbsp;and&nbsp;y&nbsp;individually, saving time and reducing the chance of calculation errors. Therefore, the value of&nbsp;x + y&nbsp;is 4, which corresponds to option (D).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1250.jpeg\" alt=\"\" class=\"wp-image-262865\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;4. This problem provides a system of two linear equations and asks for the value of the sum&nbsp;x + y. The given equations are: While you could solve for the individual values of&nbsp;x&nbsp;and&nbsp;y&nbsp;using methods like substitution or elimination, there is a more direct and efficient strategy [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-262863","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262863","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=262863"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262863\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=262863"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=262863"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=262863"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}