91Ó°ÊÓ

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$$\begin{gathered} 2x-3y-z=0 \\ 3x+2y+2z=2 \\ x+5y+3z=2 \end{gathered}$$

In Problems 46–48, graph each system of inequalities by hand. Tell whether the graph is bounded or unbounded, and label the corner points.

$\left\{\begin{array}{l}xâ‰\yen 0\\ yâ‰\yen 0\\ 2x+y≤8\\ x+2yâ‰\yen 2\end{array}\right.$

Use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

$\frac{x^3-3x^2+1}{x^2+5x+6}$

In Problems 47–54, use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition

$\frac{x^3-3x^2+1}{x^2+5x+6}$

Solve the system. Use any method you wish.

$\left\{\begin{array}{l}{x}^2-xy-2y^2=0\\ xy+x+6=0\end{array}\right.$

In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that

$$\begin{gathered} \left|\begin{array}{llr}x& y& z\\ u& v& w\\ 1& 2& 3\end{array}\right|=4 \\ \left|\begin{array}{ccc}x& y& z-x\\ u& v& w-u\\ 1& 2& 2\end{array}\right| \end{gathered}$$

Use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

$\frac{x^3}{x^2+1}$

In Problems $41-60$, use the inverses found in Problems $31-40$to solve each system of equations.

$\left\{\begin{array}{l}2x+y=-3\\ ax+ay=-a\end{array}\right.a≠0$.

In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that

$$\begin{gathered} \left|\begin{array}{llr}x& y& z\\ u& v& w\\ 1& 2& 3\end{array}\right|=4 \\ \left|\begin{array}{ccc}1& 2& 3\\ 2x& 2y& 2z\\ u-1& v-2& w-3\end{array}\right| \end{gathered}$$

In Problems 43–52, graph each system of linear inequalities by hand. Tell whether the graph is bounded or unbounded, and label the corner points

$49.\left\{\begin{array}{l}xâ‰\yen 0\\ yâ‰\yen 0\\ x+yâ‰\yen 2\\ x+y≤8\\ 2x+y≤10\end{array}\right.$