How many solutions does the system have?
x = -4y + 4
2x + 8y = 8<\/p>\n\n\n\n
A. one solution
B. two solutions
C. infinitely many solutions
D. no solution<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: C. infinitely many solutions<\/strong><\/p>\n\n\n\n To determine the number of solutions for the given system of equations, we can start by rewriting the equations:<\/p>\n\n\n\n We can substitute the expression for ( x ) from Equation 1 into Equation 2:<\/p>\n\n\n\n [ Now, distribute the 2 in the equation:<\/p>\n\n\n\n [ Combine like terms:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ The equation ( 8 = 8 ) is always true and does not depend on ( y ). This means that for any value of ( y ), there is a corresponding value of ( x ) given by Equation 1. In other words, there are infinitely many combinations of ( x ) and ( y ) that satisfy both equations.<\/p>\n\n\n\n Since we found that the second equation is satisfied for all values of ( y ), the system of equations has infinitely many solutions. Each solution corresponds to a different value of ( y ) and a specific value of ( x ) calculated from Equation 1.<\/p>\n\n\n\n Thus, the correct answer is C. infinitely many solutions<\/strong>. This type of system is called dependent, as the equations represent the same line when graphed, confirming that they have the same set of solutions.<\/p>\n","protected":false},"excerpt":{"rendered":" How many solutions does the system have?x = -4y + 42x + 8y = 8 A. one solutionB. two solutionsC. infinitely many solutionsD. no solution The Correct Answer and Explanation is : The correct answer is: C. infinitely many solutions To determine the number of solutions for the given system of equations, we can start […]<\/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-155011","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155011","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=155011"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155011\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=155011"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=155011"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=155011"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Step 1: Substitute Equation 1 into Equation 2<\/h3>\n\n\n\n
2(-4y + 4) + 8y = 8
]<\/p>\n\n\n\nStep 2: Simplify the Equation<\/h3>\n\n\n\n
-8y + 8 + 8y = 8
]<\/p>\n\n\n\n
0y + 8 = 8
]<\/p>\n\n\n\n
8 = 8
]<\/p>\n\n\n\nStep 3: Analyze the Result<\/h3>\n\n\n\n
Conclusion<\/h3>\n\n\n\n