Chapter 10

Solve by determinants. $$\begin{aligned} &3 x-2 y=-15\\\ &5 x+6 y=3 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}x+y+z &=12 \\\x-y &=2 \\\x-z &=4\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &4.92 x-8.27 y=2.58\\\ &6.93 x+2.84 y=8.36 \end{aligned}$$

Solve by determinants. $$\begin{aligned} &7 x+6 y=20\\\ &2 x+5 y=9 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{array}{l}x+y=35 \\\x+z=40 \\\y+z=45\end{array}$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} 4 n &=18-3 m \\ m &=8-2 n \end{aligned}$$

Enter the following matrices into your calculator. $$\left(\begin{array}{ll} 8 & 3 \\ 3 & 1 \end{array}\right)$$

Solve by determinants. $$\begin{aligned} &x+5 y=11\\\ &3 x+2 y=7 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&x+y+z=35\\\&x-2 y+3 z=15\\\&y-x+z=-5\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &5 p+4 q-14=0\\\ &17 p=31+3 q \end{aligned}$$

Enter the following matrices into your calculator. $$\left(\begin{array}{lll} 7 & 8 & 3 \\ 5 & 8 & 6 \\ 3 & 0 & 1 \end{array}\right)$$

Solve by determinants. $$\begin{aligned} &4 x-5 y=-34\\\ &2 x-3 y=-22 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&x+2 y+3 z=14\\\&2 x+y+2 z=10\\\&3 x+4 y-3 z=2\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &3 w=13+5 z\\\ &4 w-7 z-17=0 \end{aligned}$$

Enter the following matrices into your calculator. $$\left(\begin{array}{llll} 5 & 8 & 2 & 6 \\ 7 & 1 & 8 & 3 \\ 4 & 3 & 0 & 1 \end{array}\right)$$

Solve by determinants. $$\begin{aligned} &x=11-4 y\\\ &5 x-2 y=11 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&x+y+z=90\\\&2 x-3 y=-20\\\&2 x+3 z=145\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &3 u=5+2 v\\\ &5 v+2 u=16 \end{aligned}$$

Enter the following matrices into your calculator. $$\left(\begin{array}{llll} 4 & 3 & 0 & 1 \\ 5 & 8 & 2 & 6 \\ 3 & 1 & 2 & 7 \\ 7 & 1 & 8 & 3 \end{array}\right)$$

Solve by determinants. $$\begin{aligned} &2 x-3 y=3\\\ &4 x+5 y=39 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&x-2 y+2 z=5\\\&5 x+3 y+6 z=57\\\&x+2 y+2 z=21\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &\frac{x}{3}+\frac{y}{2}=1\\\ &\frac{x}{2}-\frac{y}{3}=-1 \end{aligned}$$

Solve by determinants. $$\begin{aligned} &\frac{x}{3}+\frac{y}{4}=8\\\ &x-y=-3 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&3 x+y=5\\\&2 y-3 z=-5\\\&x+2 z=7\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &\frac{x}{2}-\frac{3 y}{4}=0\\\ &\frac{x}{3}+\frac{y}{4}=0 \end{aligned}$$

Solve by determinants. $$\begin{aligned} &\frac{x}{2}+\frac{y}{3}=5\\\ &\frac{x}{3}+\frac{y}{2}=5 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&.2 x-4 y+3 z=10\\\&3 x+y-2 z=6\\\&x+3 y-z=20\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Three Equations in Three Unknowns. $$\begin{aligned} &x+y+z=18\\\ &x-y+z=6\\\ &x+y-z=4 \end{aligned}$$

Solve by determinants. $$\begin{aligned} &\frac{3 x}{5}+\frac{2 y}{3}=17\\\ &\frac{2 x}{3}+\frac{3 y}{4}=19 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&x-y=5\\\&y-z=-6\\\&2 x-z=2\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Three Equations in Three Unknowns. $$\begin{aligned} x+y+z &=12 \\ x-y &=2 \\ x-z &=4 \end{aligned}$$

Solve by determinants. $$\begin{aligned} &\frac{x}{7}+7 y=251\\\ &\frac{y}{7}+7 x=299 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&1.15 x+1.95 y+2.78 z=15.3\\\&2.41 x+1.16 y+3.12 z=9.66\\\&3.11 x+3.83 y-2.93 z=2.15\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Three Equations in Three Unknowns. $$\begin{aligned} &x+y=35\\\ &x+z=40\\\ &y+z=45 \end{aligned}$$

Solve by determinants. $$\begin{aligned} &7 x-4 y=81\\\ &5 x-3 y=57 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&1.52 x-2.26 y+1.83 z=4.75\\\&4.72 x+3.52 y+5.83 z=45.2\\\&1.33 x+2.61 y+3.02 z=18.5\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Three Equations in Three Unknowns. $$\begin{aligned} &x+y+z=35\\\ &x-2 y+3 z=15\\\ &y-x+z=-5 \end{aligned}$$

Solve by determinants. $$\begin{aligned} &3 x+4 y=85\\\ &5 x+4 y=107 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&x+\frac{y}{3}=5\\\&x+\frac{z}{3}=6\\\&y+\frac{z}{3}=9\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Three Equations in Three Unknowns. $$\begin{aligned} x+2 y+3 z &=14 \\ 2 x+y+2 z &=10 \\ 3 x+4 y-3 z &=2 \end{aligned}$$

Solve by determinants. $$\begin{aligned} &3 x-2 y=1\\\ &2 x+y=10 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&\frac{x}{10}+\frac{y}{5}+\frac{z}{20}=\frac{1}{4}\\\&x+y+z=6\\\&\frac{x}{3}+\frac{y}{2}+\frac{z}{6}=1\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Three Equations in Three Unknowns. $$\begin{array}{c} x+y+z=90 \\ 2 x-3 y=-20 \\ 2 x+3 z=145 \end{array}$$

Solve by determinants. $$\begin{aligned} &5 x-2 y=3\\\ &2 x+3 y=5 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&x+y+2 z+w=18\\\&x+2 y+z+w=17\\\&x+y+z+2 w=19\\\&2 x+y+z+w=16\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Three Equations in Three Unknowns. $$\begin{array}{r} x-2 y+2 z=5 \\ 5 x+3 y+6 z=57 \\ x+2 y+2 z=21 \end{array}$$

Solve by determinants. $$\begin{aligned} &y=9-3 x\\\ &x=8-2 y \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&2 x-y-z-w=0\\\&x-3 y+z+w=0\\\&x+y-4 z+w=0\\\&x+y+w=36\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Three Equations in Three Unknowns. $$\begin{aligned} 3 x+y &=5 \\ 2 y-3 z &=-5 \\ x+2 z &=7 \end{aligned}$$

Solve by determinants. $$\begin{array}{l} y=2 x-3 \\ x=19-3 y \end{array}$$