91Ó°ÊÓ

Solve each system by elimination. $$\begin{array}{l}-x+3 y=8 \\\3 x+5 y=-10\end{array}$$

Each augmented matrix is in row echelon form and represents a linear system. Use back-substitution to solve the system if possible. $$\left[\begin{array}{rrr|r} 1 & -1 & 2 & 8 \\ 0 & 1 & -4 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right]$$

Graph each inequality. $$(x-4)^{2}+y^{2} \leq 9$$

For each matrix, find \(A^{-1}\) if it exists. $$A=\left[\begin{array}{rrr} 0.8 & 0.2 & 0.1 \\ -0.2 & 0 & 0.3 \\ 0 & 0 & 0.5 \end{array}\right]$$

Find the partial fraction decomposition for each rational expression. $$\frac{3}{x(x+1)\left(x^{2}+1\right)}$$

Solve each determinant equation for \(x\). $$\operatorname{det}\left[\begin{array}{ll}x & 3 \\\x & x\end{array}\right]=4$$

Solve each system by elimination. $$\begin{array}{l}3 x-7 y=18 \\\x+5 y=-16\end{array}$$

Perform each operation if possible. $$-3\left[\begin{array}{rr}3 & 8 \\ -1 & -9\end{array}\right]+5\left[\begin{array}{rr}4 & -8 \\ 1 & 6\end{array}\right]$$

Solve each system analytically. If the equations are dependent, write the solution set in terms of the variable \(z\). $$\begin{aligned} 3 x-5 y-4 z &=-7 \\ y-z &=-13 \end{aligned}$$

Solve each system analytically. If the equations are dependent, write the solution set in terms of the variable \(z\). $$\begin{aligned} 8 x-3 y+6 z &=-2 \\ 4 x+9 y+4 z &=18 \\ 12 x-3 y+8 z &=-2 \end{aligned}$$