{"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":"2022-01-09T19:49:52","modified_gmt":"2022-01-09T19:49:52","slug":"solutions-systems-of-two-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/solutions-systems-of-two-equations\/","title":{"raw":"Solutions: Systems of Linear Equations in Two Variables","rendered":"Solutions: Systems of Linear Equations in Two Variables"},"content":{"raw":"<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.\u00a0You can solve by substitution (isolating [latex]x[\/latex] or [latex]y[\/latex] ), graphically, or by addition.\r\n\r\n5.\u00a0Yes\r\n\r\n7.\u00a0Yes\r\n\r\n9.\u00a0[latex]\\left(-1,2\\right)[\/latex]\r\n\r\n11.\u00a0[latex]\\left(-3,1\\right)[\/latex]\r\n\r\n13.\u00a0[latex]\\left(-\\frac{3}{5},0\\right)[\/latex]\r\n\r\n15.\u00a0No solutions exist.\r\n\r\n17.\u00a0[latex]\\left(\\frac{72}{5},\\frac{132}{5}\\right)[\/latex]\r\n\r\n19.\u00a0[latex]\\left(6,-6\\right)[\/latex]\r\n\r\n21.\u00a0[latex]\\left(-\\frac{1}{2},\\frac{1}{10}\\right)[\/latex]\r\n\r\n23.\u00a0No solutions exist.\r\n\r\n25.\u00a0[latex]\\left(-\\frac{1}{5},\\frac{2}{3}\\right)[\/latex]\r\n\r\n27.\u00a0[latex]\\left(x,\\frac{x+3}{2}\\right)[\/latex]\r\n\r\n29.\u00a0[latex]\\left(-4,4\\right)[\/latex]\r\n\r\n31.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{8}\\right)[\/latex]\r\n\r\n33.\u00a0[latex]\\left(\\frac{1}{6},0\\right)[\/latex]\r\n\r\n35.\u00a0[latex]\\left(x,2\\left(7x - 6\\right)\\right)[\/latex]\r\n\r\n37.\u00a0[latex]\\left(-\\frac{5}{6},\\frac{4}{3}\\right)[\/latex]\r\n\r\n39.\u00a0Consistent with one solution\r\n\r\n41.\u00a0Consistent with one solution\r\n\r\n43.\u00a0Dependent with infinitely many solutions\r\n\r\n45.\u00a0[latex]\\left(-3.08,4.91\\right)[\/latex]\r\n\r\n47.\u00a0[latex]\\left(-1.52,2.29\\right)[\/latex]\r\n\r\n49.\u00a0[latex]\\left(\\frac{A+B}{2},\\frac{A-B}{2}\\right)[\/latex]\r\n\r\n51.\u00a0[latex]\\left(\\frac{-1}{A-B},\\frac{A}{A-B}\\right)[\/latex]\r\n\r\n53.\u00a0[latex]\\left(\\frac{CE-BF}{BD-AE},\\frac{AF-CD}{BD-AE}\\right)[\/latex]\r\n\r\n&nbsp;","rendered":"<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.\u00a0You can solve by substitution (isolating [latex]x[\/latex] or [latex]y[\/latex] ), graphically, or by addition.<\/p>\n<p>5.\u00a0Yes<\/p>\n<p>7.\u00a0Yes<\/p>\n<p>9.\u00a0[latex]\\left(-1,2\\right)[\/latex]<\/p>\n<p>11.\u00a0[latex]\\left(-3,1\\right)[\/latex]<\/p>\n<p>13.\u00a0[latex]\\left(-\\frac{3}{5},0\\right)[\/latex]<\/p>\n<p>15.\u00a0No solutions exist.<\/p>\n<p>17.\u00a0[latex]\\left(\\frac{72}{5},\\frac{132}{5}\\right)[\/latex]<\/p>\n<p>19.\u00a0[latex]\\left(6,-6\\right)[\/latex]<\/p>\n<p>21.\u00a0[latex]\\left(-\\frac{1}{2},\\frac{1}{10}\\right)[\/latex]<\/p>\n<p>23.\u00a0No solutions exist.<\/p>\n<p>25.\u00a0[latex]\\left(-\\frac{1}{5},\\frac{2}{3}\\right)[\/latex]<\/p>\n<p>27.\u00a0[latex]\\left(x,\\frac{x+3}{2}\\right)[\/latex]<\/p>\n<p>29.\u00a0[latex]\\left(-4,4\\right)[\/latex]<\/p>\n<p>31.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{8}\\right)[\/latex]<\/p>\n<p>33.\u00a0[latex]\\left(\\frac{1}{6},0\\right)[\/latex]<\/p>\n<p>35.\u00a0[latex]\\left(x,2\\left(7x - 6\\right)\\right)[\/latex]<\/p>\n<p>37.\u00a0[latex]\\left(-\\frac{5}{6},\\frac{4}{3}\\right)[\/latex]<\/p>\n<p>39.\u00a0Consistent with one solution<\/p>\n<p>41.\u00a0Consistent with one solution<\/p>\n<p>43.\u00a0Dependent with infinitely many solutions<\/p>\n<p>45.\u00a0[latex]\\left(-3.08,4.91\\right)[\/latex]<\/p>\n<p>47.\u00a0[latex]\\left(-1.52,2.29\\right)[\/latex]<\/p>\n<p>49.\u00a0[latex]\\left(\\frac{A+B}{2},\\frac{A-B}{2}\\right)[\/latex]<\/p>\n<p>51.\u00a0[latex]\\left(\\frac{-1}{A-B},\\frac{A}{A-B}\\right)[\/latex]<\/p>\n<p>53.\u00a0[latex]\\left(\\frac{CE-BF}{BD-AE},\\frac{AF-CD}{BD-AE}\\right)[\/latex]<\/p>\n<p>&nbsp;<\/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":13,"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-1\/wp-json\/pressbooks\/v2\/chapters\/13206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/13206\/revisions"}],"predecessor-version":[{"id":16681,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/13206\/revisions\/16681"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/13184"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/13206\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=13206"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=13206"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=13206"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=13206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}