{"id":1530,"date":"2019-06-28T17:40:24","date_gmt":"2019-06-28T21:40:24","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1530"},"modified":"2019-11-04T13:19:32","modified_gmt":"2019-11-04T18:19:32","slug":"answer-key-5-6","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-5-6\/","title":{"raw":"Answer Key 5.6","rendered":"Answer Key 5.6"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrrl}\r\n&t&+&x&+&y&+&z&=&\\phantom{-}6 \\\\\r\n+&-t&+&x&-&y&-&z&=&-2 \\\\\r\n\\midrule\r\n&&&&&&&\\dfrac{2x}{2}&=&\\dfrac{4}{2} \\\\ \\\\\r\n&&&&&&&x&=&2 \\\\ \\\\\r\n&(-t&+&x&-&y&-&z&=&-2)(-1) \\\\\r\n&t&-&x&+&y&+&z&=&\\phantom{-}2 \\\\\r\n+&-t&+&3x&+&y&-&z&=&\\phantom{-}2 \\\\\r\n\\midrule\r\n&&&&&2x&+&2y&=&\\phantom{-}4 \\\\ \\\\\r\n&&&&&2(2)&+&2y&=&\\phantom{-}4 \\\\\r\n&&&&&-4&&&&-4 \\\\\r\n\\midrule\r\n&&&&&&&2y&=&\\phantom{-}0 \\\\\r\n&&&&&&&y&=&\\phantom{-}0\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrrrrrrl}\r\n&t&+&2x&+&2y&+&4z&=&17 \\\\\r\n+&-t&+&3x&+&y&-&z&=&2 \\\\\r\n\\midrule\r\n&&&5x&+&3y&+&3z&=&19 \\\\\r\n&&&5(2)&+&3(0)&+&3z&=&19 \\\\\r\n&&&&&10&+&3z&=&19 \\\\\r\n&&&&&-10&&&&-10 \\\\\r\n\\midrule\r\n&&&&&&&\\dfrac{3z}{3}&=&\\dfrac{9}{3} \\\\ \\\\\r\n&&&&&&&z&=&3 \\\\ \\\\\r\n&t&+&x&+&y&+&z&=&6 \\\\\r\n&t&+&2&+&0&+&3&=&6 \\\\\r\n&&&&&t&+&5&=&6 \\\\\r\n&&&&&&-&5&&-5 \\\\\r\n\\midrule\r\n&&&&&&&t&=&1 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\phantom{1} \\\\ \\)\r\n\\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&t&+&x&-&y&+&z&=&-1 \\\\\r\n+&-t&+&3x&+&y&-&z&=&1 \\\\\r\n\\midrule\r\n&&&&&&&4x&=&0 \\\\\r\n&&&&&&&x&=&0 \\\\ \\\\\r\n&&\\therefore &t&-&y&+&z&=&-1 \\\\\r\n&&&-t&+&2y&+&z&=&3 \\\\\r\n&&&-t&+&y&-&z&=&1 \\\\\r\n&&&-2t&+&y&-&3z&=&0 \\\\ \\\\\r\n&&&-t&+&2y&+&z&=&3 \\\\\r\n+&&&-t&+&y&-&z&=&1 \\\\\r\n\\midrule\r\n&&&&&-2t&+&3y&=&4 \\\\ \\\\\r\n&&&(-t&+&y&-&z&=&1)(-3) \\\\\r\n&&&3t&-&3y&+&3z&=&-3 \\\\\r\n+&&&-2t&+&y&-&3z&=&0 \\\\\r\n\\midrule\r\n&&&&&(t&-&2y&=&-3)(2) \\\\\r\n&&&&&2t&-&4y&=&-6 \\\\\r\n+&&&&&-2t&+&3y&=&4 \\\\\r\n\\midrule\r\n&&&&&&&-y&=&-2 \\\\\r\n&&&&&&&y&=&2 \\\\\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n\\\\\r\nt&-&y&+&z&=&-1 \\\\\r\nt&-&2&+&z&=&-1 \\\\\r\n&+&2&&&&+2 \\\\\r\n\\midrule\r\n&&t&+&z&=&1 \\\\ \\\\\r\n-t&+&2y&+&z&=&3 \\\\\r\n-t&+&2(2)&+&z&=&3 \\\\\r\n-t&+&4&+&z&=&3 \\\\\r\n&-&4&&&&-4 \\\\\r\n\\midrule\r\n&&-t&+&z&=&-1 \\\\\r\n+&&t&+&z&=&1 \\\\\r\n\\midrule\r\n&&&&2z&=&0 \\\\\r\n&&&&z&=&0 \\\\ \\\\\r\n&&t&+&z&=&1 \\\\\r\n&&t&+&0&=&1 \\\\\r\n&&&&t&=&1 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\begin{array}{rr}<\/li>\n
    2. \"\phantom{1} \\\"
      \n\"\begin{array}{rr}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":42,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1530","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1530","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1530\/revisions"}],"predecessor-version":[{"id":2969,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1530\/revisions\/2969"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1530\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1530"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1530"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1530"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}