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