How many solutions does this system have? Find all solutions to the system of equations.\u00c3\u201a\u00c2<\/p>\n\n\n\n
3x+2y=-1<\/p>\n\n\n\n
5x+4y=0<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n We are given the following system of linear equations:<\/p>\n\n\n\n We will use the elimination method here, where we aim to eliminate one of the variables by manipulating the equations.<\/p>\n\n\n\n First, let’s eliminate ( y ) by multiplying the first equation by 2:<\/p>\n\n\n\n [ Now, we have the modified system of equations:<\/p>\n\n\n\n Next, subtract the second equation from the first equation:<\/p>\n\n\n\n [ Now that we know ( x = -2 ), we can substitute this value back into one of the original equations to solve for ( y ). Let’s substitute into the first equation:<\/p>\n\n\n\n [ Thus, the solution to the system of equations is: The system has exactly one solution<\/strong>. The solution is the ordered pair ( \\left( -2, \\frac{5}{2} \\right) ).<\/p>\n\n\n\n The system of equations is a pair of linear equations in two variables. To solve such systems, we can use several methods: substitution, elimination, or graphing. In this case, we opted for the elimination method. We manipulated the equations to eliminate one variable and solve for the other. After solving for ( x ), we substituted that value back into one of the original equations to find ( y ). The final solution shows that the system has one unique solution, which means the lines represented by the two equations intersect at a single point on the coordinate plane.<\/p>\n","protected":false},"excerpt":{"rendered":" How many solutions does this system have? Find all solutions to the system of equations.\u00c3\u201a\u00c2 3x+2y=-1 5x+4y=0 The correct answer and explanation is : We are given the following system of linear equations: Step 1: Solve the system using substitution or elimination We will use the elimination method here, where we aim to eliminate 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-201195","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/201195","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=201195"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/201195\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=201195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=201195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=201195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Step 1: Solve the system using substitution or elimination<\/h3>\n\n\n\n
2(3x + 2y) = 2(-1)
]
[
6x + 4y = -2
]<\/p>\n\n\n\n\n
(6x + 4y) – (5x + 4y) = -2 – 0
]
[
6x – 5x = -2
]
[
x = -2
]<\/p>\n\n\n\nStep 2: Substitute ( x = -2 ) into one of the original equations<\/h3>\n\n\n\n
3x + 2y = -1
]
Substitute ( x = -2 ):
[
3(-2) + 2y = -1
]
[
-6 + 2y = -1
]
[
2y = 5
]
[
y = \\frac{5}{2}
]<\/p>\n\n\n\nStep 3: Conclusion<\/h3>\n\n\n\n
[
x = -2, \\quad y = \\frac{5}{2}
]<\/p>\n\n\n\nExplanation of the Process<\/h3>\n\n\n\n