{"id":13206,"date":"2015-11-24T18:11:12","date_gmt":"2015-11-24T18:11:12","guid":{"rendered":"https:\/\/courses.candelalearning.com\/precalcone1xcleanmaster\/?post_type=chapter&#038;p=13206"},"modified":"2019-10-04T15:13:36","modified_gmt":"2019-10-04T15:13:36","slug":"solutions-36","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/solutions-36\/","title":{"raw":"Solutions 2.4: Systems of Linear Equations: Two Variables","rendered":"Solutions 2.4: Systems of Linear Equations: Two Variables"},"content":{"raw":"<h2>Solutions to Try Its<\/h2>\r\n1.\u00a0Not a solution.\r\n\r\n2.\u00a0The solution to the system is the ordered pair [latex]\\left(-5,3\\right)[\/latex].\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/11\/03012949\/CNX_Precalc_Figure_09_01_0132.jpg\" alt=\"Two lines that cross at the point negative five, three. One line's equation is y equals four-fifths x plus 7. The other line's equation is y equals two-fifths x plus 5.\" width=\"487\" height=\"409\" \/>\r\n\r\n3.\u00a0[latex]\\left(-2,-5\\right)[\/latex]\r\n\r\n4.\u00a0[latex]\\left(-6,-2\\right)[\/latex]\r\n\r\n5.\u00a0[latex]\\left(10,-4\\right)[\/latex]\r\n\r\n6.\u00a0No solution. It is an inconsistent system.\r\n\r\n7.\u00a0The system is dependent so there are infinite solutions of the form [latex]\\left(x,2x+5\\right)[\/latex].\r\n\r\n8.\u00a0700 children, 950 adults\r\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0No, you can either have zero, one, or infinitely many. Examine graphs.\r\n\r\n3.\u00a0This means there is no realistic break-even point. By the time the company produces one unit they are already making profit.\r\n\r\n5.\u00a0You can solve by substitution (isolating [latex]x[\/latex] or [latex]y[\/latex] ), graphically, or by addition.\r\n\r\n7.\u00a0Yes\r\n\r\n9.\u00a0Yes\r\n\r\n11.\u00a0[latex]\\left(-1,2\\right)[\/latex]\r\n\r\n13.\u00a0[latex]\\left(-3,1\\right)[\/latex]\r\n\r\n15.\u00a0[latex]\\left(-\\frac{3}{5},0\\right)[\/latex]\r\n\r\n17.\u00a0No solutions exist.\r\n\r\n19.\u00a0[latex]\\left(\\frac{72}{5},\\frac{132}{5}\\right)[\/latex]\r\n\r\n21.\u00a0[latex]\\left(6,-6\\right)[\/latex]\r\n\r\n23.\u00a0[latex]\\left(-\\frac{1}{2},\\frac{1}{10}\\right)[\/latex]\r\n\r\n25.\u00a0No solutions exist.\r\n\r\n27.\u00a0[latex]\\left(-\\frac{1}{5},\\frac{2}{3}\\right)[\/latex]\r\n\r\n29.\u00a0[latex]\\left(x,\\frac{x+3}{2}\\right)[\/latex]\r\n\r\n31.\u00a0[latex]\\left(-4,4\\right)[\/latex]\r\n\r\n33.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{8}\\right)[\/latex]\r\n\r\n35.\u00a0[latex]\\left(\\frac{1}{6},0\\right)[\/latex]\r\n\r\n37.\u00a0[latex]\\left(x,2\\left(7x - 6\\right)\\right)[\/latex]\r\n\r\n39.\u00a0[latex]\\left(-\\frac{5}{6},\\frac{4}{3}\\right)[\/latex]\r\n\r\n41.\u00a0Consistent with one solution\r\n\r\n43.\u00a0Consistent with one solution\r\n\r\n45.\u00a0Dependent with infinitely many solutions\r\n\r\n47.\u00a0[latex]\\left(-3.08,4.91\\right)[\/latex]\r\n\r\n49.\u00a0[latex]\\left(-1.52,2.29\\right)[\/latex]\r\n\r\n51.\u00a0[latex]\\left(\\frac{A+B}{2},\\frac{A-B}{2}\\right)[\/latex]\r\n\r\n53.\u00a0[latex]\\left(\\frac{-1}{A-B},\\frac{A}{A-B}\\right)[\/latex]\r\n\r\n55.\u00a0[latex]\\left(\\frac{CE-BF}{BD-AE},\\frac{AF-CD}{BD-AE}\\right)[\/latex]\r\n\r\n57.\u00a0They never turn a profit.\r\n\r\n59.\u00a0[latex]\\left(1,250,100,000\\right)[\/latex]\r\n\r\n61.\u00a0The numbers are 7.5 and 20.5.\r\n\r\n63.\u00a024,000\r\n\r\n65.\u00a0790 sophomores, 805 freshman\r\n\r\n67.\u00a056 men, 74 women\r\n\r\n69.\u00a010 gallons of 10% solution, 15 gallons of 60% solution\r\n\r\n71.\u00a0Swan Peak: $750,000, Riverside: $350,000\r\n\r\n73.\u00a0$12,500 in the first account, $10,500 in the second account.\r\n\r\n75.\u00a0High-tops: 45, Low-tops: 15\r\n\r\n77.\u00a0Infinitely many solutions. We need more information.","rendered":"<h2>Solutions to Try Its<\/h2>\n<p>1.\u00a0Not a solution.<\/p>\n<p>2.\u00a0The solution to the system is the ordered pair [latex]\\left(-5,3\\right)[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/11\/03012949\/CNX_Precalc_Figure_09_01_0132.jpg\" alt=\"Two lines that cross at the point negative five, three. One line's equation is y equals four-fifths x plus 7. The other line's equation is y equals two-fifths x plus 5.\" width=\"487\" height=\"409\" \/><\/p>\n<p>3.\u00a0[latex]\\left(-2,-5\\right)[\/latex]<\/p>\n<p>4.\u00a0[latex]\\left(-6,-2\\right)[\/latex]<\/p>\n<p>5.\u00a0[latex]\\left(10,-4\\right)[\/latex]<\/p>\n<p>6.\u00a0No solution. It is an inconsistent system.<\/p>\n<p>7.\u00a0The system is dependent so there are infinite solutions of the form [latex]\\left(x,2x+5\\right)[\/latex].<\/p>\n<p>8.\u00a0700 children, 950 adults<\/p>\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1.\u00a0No, you can either have zero, one, or infinitely many. Examine graphs.<\/p>\n<p>3.\u00a0This means there is no realistic break-even point. By the time the company produces one unit they are already making profit.<\/p>\n<p>5.\u00a0You can solve by substitution (isolating [latex]x[\/latex] or [latex]y[\/latex] ), graphically, or by addition.<\/p>\n<p>7.\u00a0Yes<\/p>\n<p>9.\u00a0Yes<\/p>\n<p>11.\u00a0[latex]\\left(-1,2\\right)[\/latex]<\/p>\n<p>13.\u00a0[latex]\\left(-3,1\\right)[\/latex]<\/p>\n<p>15.\u00a0[latex]\\left(-\\frac{3}{5},0\\right)[\/latex]<\/p>\n<p>17.\u00a0No solutions exist.<\/p>\n<p>19.\u00a0[latex]\\left(\\frac{72}{5},\\frac{132}{5}\\right)[\/latex]<\/p>\n<p>21.\u00a0[latex]\\left(6,-6\\right)[\/latex]<\/p>\n<p>23.\u00a0[latex]\\left(-\\frac{1}{2},\\frac{1}{10}\\right)[\/latex]<\/p>\n<p>25.\u00a0No solutions exist.<\/p>\n<p>27.\u00a0[latex]\\left(-\\frac{1}{5},\\frac{2}{3}\\right)[\/latex]<\/p>\n<p>29.\u00a0[latex]\\left(x,\\frac{x+3}{2}\\right)[\/latex]<\/p>\n<p>31.\u00a0[latex]\\left(-4,4\\right)[\/latex]<\/p>\n<p>33.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{8}\\right)[\/latex]<\/p>\n<p>35.\u00a0[latex]\\left(\\frac{1}{6},0\\right)[\/latex]<\/p>\n<p>37.\u00a0[latex]\\left(x,2\\left(7x - 6\\right)\\right)[\/latex]<\/p>\n<p>39.\u00a0[latex]\\left(-\\frac{5}{6},\\frac{4}{3}\\right)[\/latex]<\/p>\n<p>41.\u00a0Consistent with one solution<\/p>\n<p>43.\u00a0Consistent with one solution<\/p>\n<p>45.\u00a0Dependent with infinitely many solutions<\/p>\n<p>47.\u00a0[latex]\\left(-3.08,4.91\\right)[\/latex]<\/p>\n<p>49.\u00a0[latex]\\left(-1.52,2.29\\right)[\/latex]<\/p>\n<p>51.\u00a0[latex]\\left(\\frac{A+B}{2},\\frac{A-B}{2}\\right)[\/latex]<\/p>\n<p>53.\u00a0[latex]\\left(\\frac{-1}{A-B},\\frac{A}{A-B}\\right)[\/latex]<\/p>\n<p>55.\u00a0[latex]\\left(\\frac{CE-BF}{BD-AE},\\frac{AF-CD}{BD-AE}\\right)[\/latex]<\/p>\n<p>57.\u00a0They never turn a profit.<\/p>\n<p>59.\u00a0[latex]\\left(1,250,100,000\\right)[\/latex]<\/p>\n<p>61.\u00a0The numbers are 7.5 and 20.5.<\/p>\n<p>63.\u00a024,000<\/p>\n<p>65.\u00a0790 sophomores, 805 freshman<\/p>\n<p>67.\u00a056 men, 74 women<\/p>\n<p>69.\u00a010 gallons of 10% solution, 15 gallons of 60% solution<\/p>\n<p>71.\u00a0Swan Peak: $750,000, Riverside: $350,000<\/p>\n<p>73.\u00a0$12,500 in the first account, $10,500 in the second account.<\/p>\n<p>75.\u00a0High-tops: 45, Low-tops: 15<\/p>\n<p>77.\u00a0Infinitely many solutions. We need more information.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-13206\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-13206","chapter","type-chapter","status-publish","hentry"],"part":13184,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13206\/revisions"}],"predecessor-version":[{"id":15209,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13206\/revisions\/15209"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/parts\/13184"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13206\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/media?parent=13206"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapter-type?post=13206"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/contributor?post=13206"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/license?post=13206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}