{"id":1859,"date":"2021-12-02T19:39:45","date_gmt":"2021-12-03T00:39:45","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-6\/"},"modified":"2022-11-02T10:37:58","modified_gmt":"2022-11-02T14:37:58","slug":"answer-key-5-6","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-6\/","title":{"raw":"Answer Key 5.6","rendered":"Answer Key 5.6"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrl}\n&t&+&x&+&y&+&z&=&\\phantom{-}6 \\\\\n+&-t&+&x&-&y&-&z&=&-2 \\\\\n\\hline\n&&&&&&&\\dfrac{2x}{2}&=&\\dfrac{4}{2} \\\\ \\\\\n&&&&&&&x&=&2 \\\\ \\\\\n&(-t&+&x&-&y&-&z&=&-2)(-1) \\\\\n&t&-&x&+&y&+&z&=&\\phantom{-}2 \\\\\n+&-t&+&3x&+&y&-&z&=&\\phantom{-}2 \\\\\n\\hline\n&&&&&2x&+&2y&=&\\phantom{-}4 \\\\ \\\\\n&&&&&2(2)&+&2y&=&\\phantom{-}4 \\\\\n&&&&&-4&&&&-4 \\\\\n\\hline\n&&&&&&&2y&=&\\phantom{-}0 \\\\\n&&&&&&&y&=&\\phantom{-}0\\\\ \\\\ \\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrl}\n&t&+&2x&+&2y&+&4z&=&17 \\\\\n+&-t&+&3x&+&y&-&z&=&2 \\\\\n\\hline\n&&&5x&+&3y&+&3z&=&19 \\\\\n&&&5(2)&+&3(0)&+&3z&=&19 \\\\\n&&&&&10&+&3z&=&19 \\\\\n&&&&&-10&&&&-10 \\\\\n\\hline\n&&&&&&&\\dfrac{3z}{3}&=&\\dfrac{9}{3} \\\\ \\\\\n&&&&&&&z&=&3 \\\\ \\\\\n&t&+&x&+&y&+&z&=&6 \\\\\n&t&+&2&+&0&+&3&=&6 \\\\\n&&&&&t&+&5&=&6 \\\\\n&&&&&&-&5&&-5 \\\\\n\\hline\n&&&&&&&t&=&1 \\\\\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrr}\n&t&+&x&-&y&+&z&=&-1 \\\\\n+&-t&+&3x&+&y&-&z&=&1 \\\\\n\\hline\n&&&&&&&4x&=&0 \\\\\n&&&&&&&x&=&0 \\\\ \\\\\n&&\\therefore &t&-&y&+&z&=&-1 \\\\\n&&&-t&+&2y&+&z&=&3 \\\\\n&&&-t&+&y&-&z&=&1 \\\\\n&&&-2t&+&y&-&3z&=&0 \\\\ \\\\\n&&&-t&+&2y&+&z&=&3 \\\\\n+&&&-t&+&y&-&z&=&1 \\\\\n\\hline\n&&&&&-2t&+&3y&=&4 \\\\ \\\\\n&&&(-t&+&y&-&z&=&1)(-3) \\\\\n&&&3t&-&3y&+&3z&=&-3 \\\\\n+&&&-2t&+&y&-&3z&=&0 \\\\\n\\hline\n&&&&&(t&-&2y&=&-3)(2) \\\\\n&&&&&2t&-&4y&=&-6 \\\\\n+&&&&&-2t&+&3y&=&4 \\\\\n\\hline\n&&&&&&&-y&=&-2 \\\\\n&&&&&&&y&=&2 \\\\ \\\\ \\end{array}[\/latex]\n[latex]\\begin{array}{rrrrrrrrrr}\n&&&t&-&y&+&z&=&-1 \\\\\n&&&t&-&2&+&z&=&-1 \\\\\n&&&&+&2&&&&+2 \\\\\n\\hline\n&&&&&t&+&z&=&1 \\\\ \\\\\n&&&-t&+&2y&+&z&=&3 \\\\\n&&&-t&+&2(2)&+&z&=&3 \\\\\n&&&-t&+&4&+&z&=&3 \\\\\n&&&&-&4&&&&-4 \\\\\n\\hline\n&&&&&-t&+&z&=&-1 \\\\\n&&&+&&t&+&z&=&1 \\\\\n\\hline\n&&&&&&&2z&=&0 \\\\\n&&&&&&&z&=&0 \\\\ \\\\\n&&&&&t&+&z&=&1 \\\\\n&&&&&t&+&0&=&1 \\\\\n&&&&&&&t&=&1 \\\\\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrl} &t&+&x&+&y&+&z&=&\\phantom{-}6 \\\\ +&-t&+&x&-&y&-&z&=&-2 \\\\ \\hline &&&&&&&\\dfrac{2x}{2}&=&\\dfrac{4}{2} \\\\ \\\\ &&&&&&&x&=&2 \\\\ \\\\ &(-t&+&x&-&y&-&z&=&-2)(-1) \\\\ &t&-&x&+&y&+&z&=&\\phantom{-}2 \\\\ +&-t&+&3x&+&y&-&z&=&\\phantom{-}2 \\\\ \\hline &&&&&2x&+&2y&=&\\phantom{-}4 \\\\ \\\\ &&&&&2(2)&+&2y&=&\\phantom{-}4 \\\\ &&&&&-4&&&&-4 \\\\ \\hline &&&&&&&2y&=&\\phantom{-}0 \\\\ &&&&&&&y&=&\\phantom{-}0\\\\ \\\\ \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrl} &t&+&2x&+&2y&+&4z&=&17 \\\\ +&-t&+&3x&+&y&-&z&=&2 \\\\ \\hline &&&5x&+&3y&+&3z&=&19 \\\\ &&&5(2)&+&3(0)&+&3z&=&19 \\\\ &&&&&10&+&3z&=&19 \\\\ &&&&&-10&&&&-10 \\\\ \\hline &&&&&&&\\dfrac{3z}{3}&=&\\dfrac{9}{3} \\\\ \\\\ &&&&&&&z&=&3 \\\\ \\\\ &t&+&x&+&y&+&z&=&6 \\\\ &t&+&2&+&0&+&3&=&6 \\\\ &&&&&t&+&5&=&6 \\\\ &&&&&&-&5&&-5 \\\\ \\hline &&&&&&&t&=&1 \\\\ \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrr} &t&+&x&-&y&+&z&=&-1 \\\\ +&-t&+&3x&+&y&-&z&=&1 \\\\ \\hline &&&&&&&4x&=&0 \\\\ &&&&&&&x&=&0 \\\\ \\\\ &&\\therefore &t&-&y&+&z&=&-1 \\\\ &&&-t&+&2y&+&z&=&3 \\\\ &&&-t&+&y&-&z&=&1 \\\\ &&&-2t&+&y&-&3z&=&0 \\\\ \\\\ &&&-t&+&2y&+&z&=&3 \\\\ +&&&-t&+&y&-&z&=&1 \\\\ \\hline &&&&&-2t&+&3y&=&4 \\\\ \\\\ &&&(-t&+&y&-&z&=&1)(-3) \\\\ &&&3t&-&3y&+&3z&=&-3 \\\\ +&&&-2t&+&y&-&3z&=&0 \\\\ \\hline &&&&&(t&-&2y&=&-3)(2) \\\\ &&&&&2t&-&4y&=&-6 \\\\ +&&&&&-2t&+&3y&=&4 \\\\ \\hline &&&&&&&-y&=&-2 \\\\ &&&&&&&y&=&2 \\\\ \\\\ \\end{array}[\/latex]
      \n[latex]\\begin{array}{rrrrrrrrrr} &&&t&-&y&+&z&=&-1 \\\\ &&&t&-&2&+&z&=&-1 \\\\ &&&&+&2&&&&+2 \\\\ \\hline &&&&&t&+&z&=&1 \\\\ \\\\ &&&-t&+&2y&+&z&=&3 \\\\ &&&-t&+&2(2)&+&z&=&3 \\\\ &&&-t&+&4&+&z&=&3 \\\\ &&&&-&4&&&&-4 \\\\ \\hline &&&&&-t&+&z&=&-1 \\\\ &&&+&&t&+&z&=&1 \\\\ \\hline &&&&&&&2z&=&0 \\\\ &&&&&&&z&=&0 \\\\ \\\\ &&&&&t&+&z&=&1 \\\\ &&&&&t&+&0&=&1 \\\\ &&&&&&&t&=&1 \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":47,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1859","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1859","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1859\/revisions"}],"predecessor-version":[{"id":1860,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1859\/revisions\/1860"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1859\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1859"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1859"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1859"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1859"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}