{"id":2287,"date":"2023-09-05T11:23:32","date_gmt":"2023-09-05T11:23:32","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=2287"},"modified":"2023-09-29T19:58:04","modified_gmt":"2023-09-29T19:58:04","slug":"psat-math-quiz-systems-of-equations","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/psat\/psat-math-quiz-systems-of-equations\/","title":{"rendered":"PSAT Math Quiz: Systems of Equations"},"content":{"rendered":"<p>Try our Systems of Equations quiz featuring free practice questions for the math section of the PSAT below.<\/p>\n<p><strong>Content Review:<\/strong><\/p>\n<ul>\n<li><a title=\"PSAT Math: Systems of Equations\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-systems-of-equations\/\">PSAT Math: Systems of Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.kaptest.com\/study\/psat\/psat-systems-of-equations-combinationsubstitution\/\">PSAT Math: Combination\/Substitution<\/a><\/li>\n<li><a href=\"https:\/\/www.kaptest.com\/study\/psat\/psat-math-practice-word-problems-multiple-equations\/\">PSAT Math: Word Problems and Multiple Equations<\/a><\/li>\n<\/ul>\n<p>Test your <a title=\"psat math\" href=\"https:\/\/www.kaptest.com\/psat\">PSAT readiness<\/a> by taking this PSAT Math quiz!<br \/>\n<div  class='avia-builder-widget-area clearfix  avia-builder-el-0  el_before_av_promobox  avia-builder-el-first '><div id=\"custom_html-35\" class=\"widget_text widget clearfix widget_custom_html\"><div class=\"textwidget custom-html-widget\"><div><div class='op-interactive' id='638e33288015c75952aaeb2e' data-title='PSAT Math Quiz: Systems of Equations' data-url='https:\/\/kaplannorthamerica.outgrow.us\/638e33288015c75952aaeb2e?vHeight=1' data-width='100%'><\/div><script src='\/\/dyv6f9ner1ir9.cloudfront.net\/assets\/js\/nloader.js'><\/script><script>initIframe('638e33288015c75952aaeb2e');<\/script><\/div><\/div><\/div><\/div><\/p>\n<p>\t<div   class='av_promobox  avia-button-no   avia-builder-el-1  el_after_av_sidebar  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>PSAT Math Systems of Equations Question 1<\/strong><\/p>\n<p>At a certain restaurant, there are 25 tables, and each table has either 2 or 4 chairs. If a total of 86 chairs accompany the 25 tables, how many tables have exactly 4 chairs?<\/p>\n<p>A. 12<br \/>\nB. 15<br \/>\nC. 18<br \/>\nD. 21<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-2  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-1\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-1\">Answer 1<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-1\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><b>C:\u00a0<\/b>Create a system of two linear equations where\u00a0<em>t<\/em> represents tables with 2 chairs and\u00a0<em>f<\/em> represents tables with 4 chairs. The first equation should represent the total number of\u00a0<em>tables<\/em>, each with 2 or 4 chairs, or\u00a0<em>t\u00a0<\/em>+\u00a0<em>f <\/em>= 25.<\/p>\n<p>The second equation should represent the total number of\u00a0<em>chairs<\/em>. Because\u00a0<em>t<\/em> represents tables with 2 chairs and\u00a0<em>f<\/em> represents tables with 4 chairs, the second equation should be 2<em>t<\/em> + 4<em>f\u00a0<\/em> = 86.<\/p>\n<p>Now solve the system using substitution. Solve the first equation for either variable, and substitute the result into the second equation:<\/p>\n<p><em>t\u00a0<\/em>+\u00a0<em>f<\/em> = 25 &#8211;&gt; 25 &#8211;\u00a0<em>f<\/em><br \/>\n2 (25 &#8211;<em>\u00a0 f<\/em>)<em>\u00a0+\u00a0<\/em>4<em>f<\/em> = 86<br \/>\n50 &#8211; 2<em>f + <\/em>4<em>f <\/em>= 86<br \/>\n2<em>f\u00a0<\/em>= 36<br \/>\n<em>f\u00a0<\/em>= 18<\/p>\n<p>There are 18 tables with 4 chairs each, (C). This is all the question asks for, so you don&#8217;t need to find the value of <i>t<\/i>.<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-3  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>PSAT Math Systems of Equations Question 2<\/strong><\/p>\n<p>If (<i>x<\/i>,\u00a0<i>y<\/i>) is the solution to the system of equations graphed in the figure, what is the value of\u00a0<i>x<\/i>\u00a0+\u00a0<i>y ?<\/i><\/p>\n<p><div  class='avia-image-container  av-styling-    avia-builder-el-4  avia-builder-el-no-sibling  avia-align-left '  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\"  ><div class='avia-image-container-inner'><div class='avia-image-overlay-wrap'><img class='wp-image-44911 avia-img-lazy-loading-not-44911 avia_image' src=\"https:\/\/wpapp.kaptest.com\/study\/wp-content\/uploads\/WwW4hCYFSY2tDsv79oob_PSAT_Math_Quiz_systems_of_equations_question_3_graph.png\" alt='' title='WwW4hCYFSY2tDsv79oob_PSAT_Math_Quiz_systems_of_equations_question_3_graph' height=\"498\" width=\"896\"  itemprop=\"thumbnailUrl\"  \/><\/div><\/div><\/div><\/p>\n<p>A. -2<br \/>\nB. -1<br \/>\nC. 1<br \/>\nD. 4<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-5  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-2\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-2\">Answer 2<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-2\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>C:\u00a0<\/strong>Graphically, the solution to a system of linear equations is the point where the lines intersect. Jot down the coordinates of the point on the graph where the two lines intersect, (01, 2). The question asks for the sum of\u00a0<em>x\u00a0<\/em>+\u00a0<em>y<\/em>, so add\u00a0the coordinates to get =1 + 2 = 1. Choice (C) is correct.<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-6  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>PSAT Math Systems of Equations Question 3<\/strong><\/p>\n<p>Two turkey burgers and a bottle of water cost $3.25. If three turkey burgers and a bottle of water cost $4.50, what is the cost of two bottles of water?<\/p>\n<p>A. $0.75<br \/>\nB. $1.25<br \/>\nC. $1.50<br \/>\nD. $3.00<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-7  el_after_av_promobox  avia-builder-el-last \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-3\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-3\">Answer 3<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-3\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>C:\u00a0<\/strong>Translate English into math to write a system of equations with\u00a0<em>t<\/em> being the cost of a turkey burger and\u00a0<em>w<\/em> equaling the cost of a bottle of water. The first statement is translated as 2<em>t<\/em> +\u00a0<em>w<\/em> = $3.25 and the second as 3<em>t<\/em> +\u00a0<em>w<\/em> = $4.50.<\/p>\n<p>The system is:<\/p>\n<p>2<em>t<\/em> +\u00a0<em>w<\/em> = 3.25<br \/>\n3<em>t<\/em> +\u00a0<em>w<\/em> = 4.50<\/p>\n<p>You could solve the system using substitution, but combination is quicker in this question because subtracting the first equation from the second eliminates\u00a0<em>w<\/em> and you can solve for\u00a0<em>t<\/em>:<\/p>\n<p>3<em>t<\/em> +\u00a0<em>w\u00a0<\/em>= 4.50<br \/>\n&#8211; (2<em>t<\/em> +\u00a0<em>w<\/em> = 3.25)<br \/>\n<em>t\u00a0<\/em>= 1.25<\/p>\n<p>Substitute this value for\u00a0<em>t<\/em> in the first equation and solve for\u00a0<em>w<\/em>:<\/p>\n<p>2(1.25) +\u00a0<em>w<\/em> = 3.25<br \/>\n2.5 +\u00a0<em>w<\/em> = 3.25<br \/>\n<em>w<\/em> = 0.75<\/p>\n<p>Two bottles of water would cost 2 x $0.75 = $1.50, which is (C).<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><\/p>\n<p>Previous: <a title=\"PSAT Math Quiz: Equations and Word Problems\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-quiz-equations-and-word-problems\/\">PSAT Math Quiz: Equations and Word Problems<\/a><br \/>\nNext: <a title=\"PSAT Math Quiz: Rates, Ratios, Proportions and Percents\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-quiz-rates-ratios-proportions-and-percents\/\">PSAT Math Quiz: Rates, Ratios, Proportions, and Percents<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Try our Systems of Equations quiz featuring free practice questions for the math section of the PSAT below. Content Review: PSAT Math: Systems of Equations PSAT Math: Combination\/Substitution PSAT Math: Word Problems and Multiple Equations Test your PSAT readiness by taking this PSAT Math quiz! Previous: PSAT Math Quiz: Equations and Word Problems Next: PSAT [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":42037,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[240],"tags":[195,310,311],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2287"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=2287"}],"version-history":[{"count":17,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2287\/revisions"}],"predecessor-version":[{"id":44922,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2287\/revisions\/44922"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/42037"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=2287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=2287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=2287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}