91Ó°ÊÓ

Use matrices to solve each system of equations. $$ \left\\{\begin{array}{l} x+y+z=6 \\ x+2 y+z=8 \\ x+y+2 z=9 \end{array}\right. $$

Evaluate each determinant. $$ \left|\begin{array}{rrr} 1 & 1 & 2 \\ 2 & 1 & -2 \\ 3 & 1 & 3 \end{array}\right| $$

Solve each system by graphing. See Example 5 . $$ \left\\{\begin{array}{l} x=y+3 \\ \frac{1}{4} x-\frac{1}{6} y=\frac{1}{3} \end{array}\right. $$

Solve each system using elimination. $$ \left\\{\begin{array}{l} 2 x+y=4 \\ -x-2 y+8 z=7 \\ -y+4 z=5 \end{array}\right. $$

Measurement. \(\Lambda\) furlong is a measure of distance and is used to express the length of certain horse races. A fathom is a measure of distance and is used to express depths of water. Four furlongs and five fathoms is a total of \(2,670\) feet. Five furlongs and four fathoms is a total of \(3,324\) feet. Find the length of a furlong and a fathom.

Solve each system by elimination. See Example 5 . $$ \left\\{\begin{array}{l} c-2 d=29 \\ 2(c-5)=d-21 \end{array}\right. $$

Evaluate each determinant. $$ \left|\begin{array}{rrr} -2 & 5 & 1 \\ 0 & 3 & 4 \\ -1 & 2 & 6 \end{array}\right| $$

Use matrices to solve each system of equations. $$ \left\\{\begin{array}{l} 3 x+y-3 z=5 \\ x-2 y+4 z=10 \\ x+y+z=13 \end{array}\right. $$

Solve each system by elimination. See Example 5 . $$ \left\\{\begin{array}{l} 2(x+y)+1=0 \\ 3 x+4 y=0 \end{array}\right. $$

Solve each system using substitution. $$ \left\\{\begin{array}{l} r+s-3 t=21 \\ r+4 s=9 \\ 5 s+t=-4 \end{array}\right. $$