91Ó°ÊÓ

Graph the solution set of each system of inequalities. $$\begin{aligned}&x+2 y \leq 4\\\&y \geq x^{2}-1\end{aligned}$$

Graph the solution set of each system of inequalities. $$\begin{aligned}&x+y \leq 9\\\&x \leq-y^{2}\end{aligned}$$

Give all solutions of each nonlinear system of equations, including those with nonreal complex components. $$\begin{aligned} &x^{2}+3 x y-y^{2}=12\\\ &x^{2}-y^{2}=-12 \end{aligned}$$

Solve each equation for \(x\). $$\left|\begin{array}{rr} -0.5 & 2 \\ x & x \end{array}\right|=0$$

Solve each system by using the inverse of the coefficient matrix. $$\begin{aligned} &x+3 y=-12\\\ &2 x-y=11 \end{aligned}$$

Solve each system. State whether it is inconsistent or has infinitely many solutions. If the system has infinitely many solutions, write the solution set with y arbitrary. $$\begin{array}{r} 2 x-8 y=4 \\ x-4 y=2 \end{array}$$

$$\text {Let } A=\left[\begin{array}{rr} -2 & 4 \\ 0 & 3 \end{array}\right] \text { and } B=\left[\begin{array}{rr} -6 & 2 \\ 4 & 0 \end{array}\right] . \text { Find each of the following.}$$ $$-3 B$$

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, give the solution with y arbitrary. For systems in three variables with infinitely many solutions, give the solution with z arbitrary. $$\begin{aligned}&5 x-3 y+z=1\\\&2 x+y-z=4\end{aligned}$$

Give all solutions of each nonlinear system of equations, including those with nonreal complex components. $$\begin{aligned} &x^{2}+y^{2}=25\\\ &|x|-y=5 \end{aligned}$$

$$\text {Let } A=\left[\begin{array}{rr} -2 & 4 \\ 0 & 3 \end{array}\right] \text { and } B=\left[\begin{array}{rr} -6 & 2 \\ 4 & 0 \end{array}\right] . \text { Find each of the following.}$$ $$\frac{3}{2} B$$