91Ó°ÊÓ

What is a system of linear equations in three variables?

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. \(2 x+5 y=-4\) \(3 x-y=11\)

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$ \begin{aligned}&4 x-5 y \geq-20\\\&x \geq-3\end{aligned} $$

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

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

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. \(x+3 y=2\) \(3 x+9 y=6\)

Solve each system by the method of your choice. $$\begin{aligned} &x^{2}+(y-2)^{2}=4\\\ &x^{2}-2 y=0 \end{aligned}$$

Solve each system by the method of your choice. $$\begin{aligned} &x^{2}-y^{2}-4 x+6 y-4=0\\\ &x^{2}+y^{2}-4 x-6 y+12=0 \end{aligned}$$

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. $$\frac{x^{2}+2 x+3}{\left(x^{2}+4\right)^{2}}$$