Answer Key 5.7
- [latex]\begin{array}{rr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \begin{array}{rrrrr} &&3H&=&30 \\ &&H&=&10 \\ \\ H&+&4S&=&18 \\ 10&+&4S&=&18 \\ -10&&&&-10 \\ \hline &&\dfrac{4S}{4}&=&\dfrac{8}{4} \\ \\ &&S&=&2 \end{array} & \hspace{0.25in} \begin{array}{rrrcrrr} \\ \\ &&2S&-&2B&=&2 \\ &&2(2)&-&2B&=&2 \\ &&4&-&2B&=&2 \\ &&-4&&&&-4 \\ \hline &&&&\dfrac{-2B}{-2}&=&\dfrac{-2}{-2} \\ \\ &&&&B&=&1 \\ \\ B&+&H&\times &S&=&? \\ 1&+&(10&\times &2)&=&? \\ &&1&+&20&=&21 \end{array} \end{array}[/latex]
- [latex]\begin{array}{rr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \begin{array}{rrrrr} &&3B&=&30 \\ &&B&=&10 \\ \\ B&+&2H&=&20 \\ 10&+&2H&=&20 \\ -10&&&&-10 \\ \hline &&\dfrac{2H}{2}&=&\dfrac{10}{2} \\ \\ &&H&=&5 \end{array} & \hspace{0.25in} \begin{array}{rrrrrrr} &&H&+&4M&=&9 \\ &&5&+&4M&=&9 \\ &&-5&&&&-5 \\ \hline &&&&4M&=&4 \\ &&&&M&=&1 \\ \\ H&+&M&\times &B&=&? \\ 10&+&(5&\times &1)&=&? \\ &&10&+&5&=&15 \end{array} \end{array}[/latex]
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[latex]\begin{array}{rrrrrrrrrl} \text{Row 2}&-a&-&2b&-&2c&+&2d&=&-8 \\ \text{Row 3}&2a&-&b&-&c&-&d&=&\phantom{-}5 \\ \text{Column 1}&a&-&b&+&c&+&2d&=&-1 \\ \text{Column 3}&a&-&2b&-&c&-&d&=&\phantom{-}3 \\ \\ &(-a&-&2b&-&2c&+&2d&=&-8)(2) \\ &-2a&-&4b&-&4c&+&4d&=&-16 \\ +&2a&-&b&-&c&-&d&=&\phantom{-0}5 \\ \hline &&&-5b&-&5c&+&3d&=&-11 \\ \\ &-a&-&2b&-&2c&+&2d&=&-8 \\ +&a&-&b&+&c&+&2d&=&-1 \\ \hline &&&-3b&-&c&+&4d&=&-9 \\ \\ &-a&-&2b&-&2c&+&2d&=&-8 \\ +&a&-&2b&-&c&-&d&=&\phantom{-}3 \\ \hline &&&(-4b&-&3c&+&d&=&-5)(-4) \\ &&&16b&+&12c&-&4d&=&20 \\ &&+&-3b&-&c&+&4d&=&-9 \\ \hline &&&&&13b&+&11c&=&11 \\ \\ &&&(-4b&-&3c&+&d&=&-5)(-3) \\ &&&12b&+&9c&-&3d&=&\phantom{-}15 \\ &&+&-5b&-&5c&+&3d&=&-11 \\ \hline &&&&&7b&+&4c&=&4 \end{array}[/latex]
[latex]\phantom{1} \\ \\ \\ \\[/latex]
[latex]\begin{array}{rrrrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&&&(13b&+&11c&=&11)(-4) \\ &&&&(\phantom{0}7b&+&4c&=&\phantom{0}4)(11) \\ \\ &&&&-52b&-&44c&=&-44 \\ &&&+&77b&+&44c&=&\phantom{-}44 \\ \hline &&&&&&25b&=&0 \\ &&&&&&b&=&0 \\ \\ &&&&7b&+&4c&=&4 \\ &&&&7(0)&+&4c&=&4 \\ &&&&&&\dfrac{4c}{4}&=&\dfrac{4}{4} \\ \\ &&&&&&c&=&1 \\ \\ &&-4b&-&3c&+&d&=&-5 \\ &&-4(0)&-&3(1)&+&d&=&-5 \\ &&&&-3&+&d&=&-5 \\ &&&&+3&&&&+3 \\ \hline &&&&&&d&=&-2 \\ \\ a&-&2b&-&c&-&d&=&\phantom{-}3 \\ a&-&2(0)&-&1&-&(-2)&=&\phantom{-}3 \\ &&a&-&1&+&2&=&\phantom{-}3 \\ &&&&a&+&1&=&\phantom{-}3 \\ &&&&&-&1&&-1 \\ \hline &&&&&&a&=&2 \end{array}[/latex]
