91Ó°ÊÓ

Solve the system by Gaussian elimination. \(\frac{3}{4} x-\frac{3}{5} y=4\) \(\frac{1}{4} x+\frac{2}{3} y=1\)

Solve each system by any method. $$ \begin{array}{c} 5 x+9 y=16 \\ x+2 y=4 \end{array} $$

Use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. \(A=\left[\begin{array}{rr}-10 & 20 \\ 5 & 25\end{array}\right], B=\left[\begin{array}{rr}40 & 10 \\ -20 & 30\end{array}\right], C=\left[\begin{array}{rr}-1 & 0 \\ 0 & -1 \\ 1 & 0\end{array}\right]\) \(B A\)

For the following exercises, use any method to solve the nonlinear system. $$\begin{aligned} x^{2}+y^{2} &=1 \\ y^{2} &=x^{2} \end{aligned}$$

For the following exercises, solve the system using the inverse of a \(2 \times 2\) matrix. $$\begin{array}{l}{-2 x+3 y=\frac{3}{10}} \\ {-x+5 y=\frac{1}{2}}\end{array}$$

Solve each system by Gaussian elimination. $$ \begin{array}{l} \frac{1}{2} x-\frac{1}{4} y+\frac{3}{4} z=0 \\ \frac{1}{4} x-\frac{1}{10} y+\frac{2}{5} z=-2 \\ \frac{1}{8} x+\frac{1}{5} y-\frac{1}{8} z=2 \end{array} $$

For the following exercises, solve the system of linear equations using Cramer's Rule. $$ \begin{array}{r} 4 x-5 y=7 \\ -3 x+9 y=0 \end{array} $$

Solve the system by Gaussian elimination. \(\frac{1}{4} x-\frac{2}{3} y=-1\) \(\frac{1}{2} x+\frac{1}{3} y=3\)

Solve each system by any method. $$ \begin{array}{l} 6 x-8 y=-0.6 \\ 3 x+2 y=0.9 \end{array} $$

For the following exercises, solve each system by Gaussian elimination. $$ \begin{array}{l}{\frac{1}{2} x-\frac{1}{4} y+\frac{3}{4} z=0} \\ {\frac{1}{4} x-\frac{1}{10} y+\frac{2}{5} z=-2} \\ {\frac{1}{8} x+\frac{1}{5} y-\frac{1}{8} z=2}\end{array} $$