91Ó°ÊÓ

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(4 x-2 y=2\) \(2 x-y=1\)

Solve each system by the method of your choice. $$\begin{aligned} &y=(x+3)^{2}\\\ &x+2 y=-2 \end{aligned}$$

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(\frac{x}{4}-\frac{y}{4}=-1\) \(x+4 y=-9\)

Write the partial fraction decomposition of each rational expression. $$\frac{x^{3}-4 x^{2}+9 x-5}{\left(x^{2}-2 x+3\right)^{2}}$$

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$ \begin{aligned}&x+y>4\\\&x+y>-1\end{aligned} $$

Solve each system by the method of your choice. $$\begin{aligned} &(x-1)^{2}+(y+1)^{2}=5\\\ &2 x-y=3 \end{aligned}$$

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(\frac{x}{6}-\frac{y}{2}=\frac{1}{3}\) \(x+2 y=-3\)

Write the partial fraction decomposition of each rational expression. $$\frac{3 x^{3}-6 x^{2}+7 x-2}{\left(x^{2}-2 x+2\right)^{2}}$$

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$ \begin{aligned}&x+y>3\\\&x+y>-2\end{aligned} $$

Write the partial fraction decomposition of each rational expression. $$\frac{4 x^{2}+3 x+14}{x^{3}-8}$$