To solve the system of equations:<\/p>\n\n\n\n
- \n
- 2x\u2212y=72x – y = 72x\u2212y=7<\/li>\n\n\n\n
- x+y=2x + y = 2x+y=2<\/li>\n<\/ol>\n\n\n\n
We can use either the substitution method or the elimination method. Let\u2019s solve it step by step using the substitution method<\/strong>.<\/p>\n\n\n\n
Step 1: Solve one equation for one variable<\/h3>\n\n\n\n
We\u2019ll start by solving the second equation for yyy:x+y=2x + y = 2x+y=2<\/p>\n\n\n\n
Solving for yyy, we get:y=2\u2212xy = 2 – xy=2\u2212x<\/p>\n\n\n\n
Step 2: Substitute the expression for yyy into the first equation<\/h3>\n\n\n\n
Now, substitute y=2\u2212xy = 2 – xy=2\u2212x into the first equation 2x\u2212y=72x – y = 72x\u2212y=7:2x\u2212(2\u2212x)=72x – (2 – x) = 72x\u2212(2\u2212x)=7<\/p>\n\n\n\n
Step 3: Simplify the equation<\/h3>\n\n\n\n
Distribute the negative sign:2x\u22122+x=72x – 2 + x = 72x\u22122+x=7<\/p>\n\n\n\n
Combine like terms:3x\u22122=73x – 2 = 73x\u22122=7<\/p>\n\n\n\n
Step 4: Solve for xxx<\/h3>\n\n\n\n
Now, add 2 to both sides to isolate the term with xxx:3x=93x = 93x=9<\/p>\n\n\n\n
Finally, divide by 3:x=3x = 3x=3<\/p>\n\n\n\n
Step 5: Solve for yyy<\/h3>\n\n\n\n
Now that we have x=3x = 3x=3, substitute this value back into the equation y=2\u2212xy = 2 – xy=2\u2212x:y=2\u22123=\u22121y = 2 – 3 = -1y=2\u22123=\u22121<\/p>\n\n\n\n
Final Answer<\/h3>\n\n\n\n
The solution to the system of equations is:x=3,y=\u22121x = 3, \\quad y = -1x=3,y=\u22121<\/p>\n\n\n\n
Verification:<\/h3>\n\n\n\n
To verify, substitute x=3x = 3x=3 and y=\u22121y = -1y=\u22121 into the original equations:<\/p>\n\n\n\n
- \n
- 2x\u2212y=72x – y = 72x\u2212y=7 becomes 2(3)\u2212(\u22121)=6+1=72(3) – (-1) = 6 + 1 = 72(3)\u2212(\u22121)=6+1=7, which is correct.<\/li>\n\n\n\n
- x+y=2x + y = 2x+y=2 becomes 3+(\u22121)=23 + (-1) = 23+(\u22121)=2, which is also correct.<\/li>\n<\/ol>\n\n\n\n
Therefore, the solution x=3x = 3x=3 and y=\u22121y = -1y=\u22121 is correct!<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1820.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"Solve the system of equations. 2x – y = 7 x + y = 2 The Correct Answer and Explanation is: To solve the system of equations: We can use either the substitution method or the elimination method. Let\u2019s solve it step by step using the substitution method. Step 1: Solve one equation for one […]<\/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-268830","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268830","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=268830"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268830\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=268830"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=268830"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=268830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}