What is the solution to the system of equations below?
x + 3 y = 15 and 4 x + 2 y = 30
(6, 3)
(3, 6)
(7, \u20136)
(\u20136, 7)<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: (6, 3)<\/strong>.<\/p>\n\n\n\n To solve the system of equations given by:<\/p>\n\n\n\n we can use the substitution or elimination method. Here, I’ll demonstrate the elimination method.<\/p>\n\n\n\n First, we can manipulate Equation 1 to express one variable in terms of the other. Let\u2019s solve for ( x ) in terms of ( y ):<\/p>\n\n\n\n [ Next, we can substitute Equation 3 into Equation 2:<\/p>\n\n\n\n [ Now, distribute ( 4 ):<\/p>\n\n\n\n [ Combine like terms:<\/p>\n\n\n\n [ Now, isolate ( y ) by subtracting ( 60 ) from both sides:<\/p>\n\n\n\n [ Now, divide both sides by ( -10 ):<\/p>\n\n\n\n [ Next, substitute ( y = 3 ) back into Equation 3 to find ( x ):<\/p>\n\n\n\n [ Thus, the solution to the system of equations is ( (6, 3) ).<\/p>\n\n\n\n To verify, we can substitute ( x = 6 ) and ( y = 3 ) back into both original equations:<\/p>\n\n\n\n Since both equations are satisfied, the solution ( (6, 3) ) is correct. Thus, the answer to the system of equations is (6, 3)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the solution to the system of equations below?x + 3 y = 15 and 4 x + 2 y = 30(6, 3)(3, 6)(7, \u20136)(\u20136, 7) The Correct Answer and Explanation is : The correct answer is: (6, 3). To solve the system of equations given by: we can use the substitution or elimination […]<\/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-155037","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155037","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=155037"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155037\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=155037"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=155037"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=155037"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
x = 15 – 3y \\tag{Equation 3}
]<\/p>\n\n\n\n
4(15 – 3y) + 2y = 30
]<\/p>\n\n\n\n
60 – 12y + 2y = 30
]<\/p>\n\n\n\n
60 – 10y = 30
]<\/p>\n\n\n\n
-10y = 30 – 60
]
[
-10y = -30
]<\/p>\n\n\n\n
y = 3
]<\/p>\n\n\n\n
x = 15 – 3(3)
]
[
x = 15 – 9
]
[
x = 6
]<\/p>\n\n\n\n\n
[
6 + 3(3) = 6 + 9 = 15 \\quad \\text{(True)}
]<\/li>\n\n\n\n
[
4(6) + 2(3) = 24 + 6 = 30 \\quad \\text{(True)}
]<\/li>\n<\/ol>\n\n\n\n