How many solutions does the system have? y=\u22122x+4
y=x^2\u22122x+4<\/p>\n\n\n\n
Enter your answer in the box.<\/p>\n\n\n\n
The correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To determine how many solutions the system of equations has, we need to solve the system:<\/p>\n\n\n\n Since both equations are set equal to ( y ), we can set them equal to each other to find the points where they intersect (i.e., the values of ( x ) where the two equations have the same ( y )-value):<\/p>\n\n\n\n [ Now, simplify the equation by subtracting ( (-2x + 4) ) from both sides:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Now, solve for ( x ):<\/p>\n\n\n\n [ So, ( x = 0 ) is the only solution for ( x ). To find the corresponding value of ( y ), substitute ( x = 0 ) into either equation. We’ll use the first equation:<\/p>\n\n\n\n [ Thus, the solution is ( (0, 4) ).<\/p>\n\n\n\n Since we found only one value of ( x ) that satisfies both equations, the system has one solution<\/strong>, which is ( (0, 4) ).<\/p>\n\n\n\n This system consists of a linear equation ( y = -2x + 4 ), which represents a straight line, and a quadratic equation ( y = x^2 – 2x + 4 ), which represents a parabola. The number of solutions to this system corresponds to the number of intersection points between the line and the parabola.<\/p>\n\n\n\n After solving, we found that the equations intersect at exactly one point, ( (0, 4) ), which means the system has one solution<\/strong>. The quadratic equation forms a parabola that touches the line at one point, which is known as a “tangent” intersection. Therefore, the system has exactly one solution<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" How many solutions does the system have? y=\u22122x+4y=x^2\u22122x+4 Enter your answer in the box. The correct Answer and Explanation is: To determine how many solutions the system of equations has, we need to solve the system: Since both equations are set equal to ( y ), we can set them equal to each other to […]<\/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-151584","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151584","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=151584"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151584\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=151584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=151584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=151584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
-2x + 4 = x^2 – 2x + 4
]<\/p>\n\n\n\n
0 = x^2
]<\/p>\n\n\n\n
x^2 = 0
]<\/p>\n\n\n\n
x = 0
]<\/p>\n\n\n\n
y = -2(0) + 4 = 4
]<\/p>\n\n\n\nHow many solutions?<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n