91Ó°ÊÓ

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. $$\left\\{\begin{array}{l}\frac{x}{4}-\frac{y}{4}=-1 \\\x+4 y=-9\end{array}\right.$$

In Exercises \(9-42,\) 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 system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}x-y \leq 1 \\\x \geq 2\end{array}\right.$$

If \(f(x)=5 x^{2}-6 x+1,\) find \(\frac{f(x+h)-f(x)}{h}\)

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

A person invested \(\$ 6700\) for one year, part at \(8 \%,\) part at \(10 \%,\) and the remainder at \(12 \% .\) The total annual income from these investments was \(\$ 716 .\) The amount of money invested at \(12 \%\) was \(\$ 300\) more than the amount invested at \(8 \%\) and \(10 \%\) combined. Find the amount invested at each rate.

Graph the solution set of system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{c}4 x-5 y \geq-20 \\\x \geq-3\end{array}\right.$$

In Exercises \(9-42,\) write the partial fraction decomposition of each rational expression. $$\frac{3 x^{3}-6 x^{2}+7 x-2}{\left(x^{2}-2 x+2\right)^{2}}$$

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

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. $$\left\\{\begin{array}{l}\frac{x}{6}-\frac{y}{2}=\frac{1}{3} \\\x+2 y=-3\end{array}\right.$$