91Ó°ÊÓ

Use Gaussian elimination to solve the system of linear equations. If there is no solution, state that the system is inconsistent. $$\left\\{\begin{aligned} 4 x+z &=0 \\ 3 x-5 y+z &=-1 \\ x+5 y &=-1 \end{aligned}\right.$$

Apply elementary roes operations to a matrix to solve the system of equations. If there is no solution, state that the system is inconsistent. $$\left\\{\begin{array}{rr}-x-y= & -10 \\\3 x+4 y= & 24\end{array}\right.$$

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

Solve for \(x\). $$\left|\begin{array}{rr} 5 & -1 \\ x & 2 \end{array}\right|=13$$

Use elimination to solve each system of equations. Check your solution. $$\left\\{\begin{array}{l} -2 x \quad=-4 \\ -4 x+3 y=-3 \end{array}\right.$$

Apply elementary roes operations to a matrix to solve the system of equations. If there is no solution, state that the system is inconsistent. $$\begin{aligned}&-2 x+y=-5\\\&4 x-y=6\end{aligned}$$

Use Gaussian elimination to solve the system of linear equations. If there is no solution, state that the system is inconsistent. $$\left\\{\begin{array}{c} 5 x+6 y-2 z=2 \\ 2 x-y+z=2 \\ x+4 y-2 z=0 \end{array}\right.$$

Use elimination to solve each system of equations. Check your solution. $$\left\\{\begin{aligned} -2 x-3 y &=0 \\ 3 x+5 y &=-2 \end{aligned}\right.$$

Write the partial fraction decomposition of each rational expression. $$\frac{-2 x+6}{x^{2}-2 x+1}$$

In Exercises \(1-34\), find all real solutions of the system of equations. If no real solution exists, so state. $$\left\\{\begin{array}{r} x^{2}+(y-1)^{2}=9 \\ x^{2}+\quad y^{2}=4 \end{array}\right.$$