{"id":161049,"date":"2024-11-03T21:00:17","date_gmt":"2024-11-03T21:00:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=161049"},"modified":"2024-11-03T21:00:19","modified_gmt":"2024-11-03T21:00:19","slug":"how-many-solutions-does-the-system-of-equations-have","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/03\/how-many-solutions-does-the-system-of-equations-have\/","title":{"rendered":"How many solutions does the system of equations have"},"content":{"rendered":"\n<p>How many solutions does the system of equations have?<br>y=\u22122x+4<\/p>\n\n\n\n<p>y=2x<br>A. One solution <\/p>\n\n\n\n<p>B. Infinitely many solutions <\/p>\n\n\n\n<p>C. No solution<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine the number of solutions for the system of equations given by:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(y = -2x + 4)<\/li>\n\n\n\n<li>(y = 2x)<\/li>\n<\/ol>\n\n\n\n<p>we can analyze the equations graphically or algebraically.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Graphical Interpretation<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>First Equation<\/strong>: The first equation (y = -2x + 4) is in slope-intercept form ((y = mx + b)), where the slope ((m)) is (-2) and the y-intercept ((b)) is (4). This means the line descends steeply from left to right, crossing the y-axis at (y = 4).<\/li>\n\n\n\n<li><strong>Second Equation<\/strong>: The second equation (y = 2x) also follows the slope-intercept form, with a slope of (2) and a y-intercept of (0). This line ascends from left to right, crossing the origin (0,0).<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Algebraic Method<\/h3>\n\n\n\n<p>To find the intersection point (solution) of these two lines, we set the equations equal to each other:<\/p>\n\n\n\n<p>[<br>-2x + 4 = 2x<br>]<\/p>\n\n\n\n<p>Next, we solve for (x):<\/p>\n\n\n\n<p>[<br>4 = 2x + 2x<br>]<br>[<br>4 = 4x<br>]<br>[<br>x = 1<br>]<\/p>\n\n\n\n<p>Now that we have (x = 1), we can substitute this value back into either original equation to find (y). Using the second equation:<\/p>\n\n\n\n<p>[<br>y = 2(1) = 2<br>]<\/p>\n\n\n\n<p>Thus, the point of intersection is ((1, 2)). This means there is exactly one point where these two lines meet.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Since the two lines have different slopes (the first has a slope of (-2) while the second has a slope of (2)), they are not parallel and will intersect at exactly one point. Therefore, the system of equations has <strong>one solution<\/strong>.<\/p>\n\n\n\n<p>The correct answer is <strong>A. One solution<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How many solutions does the system of equations have?y=\u22122x+4 y=2xA. One solution B. Infinitely many solutions C. No solution The Correct Answer and Explanation is: To determine the number of solutions for the system of equations given by: we can analyze the equations graphically or algebraically. Graphical Interpretation Algebraic Method To find the intersection point [&hellip;]<\/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-161049","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161049","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=161049"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161049\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=161049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=161049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=161049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}