91Ó°ÊÓ

For the following exercises, determine whether the ordered triple given is the solution to the system of equations. $$ \begin{aligned} 6 x-7 y+z &=2 \\\\-x-y+3 z &=4 \quad \text { and }(4,2,-6) \\\ 2 x+y-z &=1 \end{aligned} $$

Determine whether the ordered triple given is the solution to the system of equations. $$ \begin{aligned} 6 x-7 y+z &=2 \\ -x-y+3 z &=4 \quad \text { and }(4,2,-6) \\ 2 x+y-z &=1 \end{aligned} $$

For the following exercises, solve the system of nonlinear equations using substitution. $$\begin{aligned} y &=x \\ x^{2}+y^{2} &=9 \end{aligned}$$

For the following exercises, write the augmented matrix for the linear system. $$ \begin{aligned} 3 x+2 y+10 z &=3 \\\\-6 x+2 y+5 z &=13 \\ 4 x+z &=18 \end{aligned} $$

Find the decomposition of the partial fraction for the nonrepeating linear factors. \(\frac{-x-24}{x^{2}-2 x-24}\)

Solve the system of nonlinear equations using substitution. $$ \begin{aligned} y &=x \\ x^{2}+y^{2} &=9 \end{aligned} $$

Write the augmented matrix for the linear system. \(\begin{aligned} \text { 8. } 3 x+2 y+10 z &=3 \\\\-6 x+2 y+5 z &=13 \\ 4 x+z &=18 \end{aligned}\)

Use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. \(A=\left[\begin{array}{ll}1 & 3 \\ 0 & 7\end{array}\right], B=\left[\begin{array}{rr}2 & 14 \\ 22 & 6\end{array}\right], C=\left[\begin{array}{rr}1 & 5 \\ 8 & 92 \\ 12 & 6\end{array}\right], D=\left[\begin{array}{rr}10 & 14 \\ 7 & 2 \\ 5 & 61\end{array}\right], E=\left[\begin{array}{rr}6 & 12 \\ 14 & 5\end{array}\right], F=\left[\begin{array}{rr}0 & 9 \\ 78 & 17 \\ 15 & 4\end{array}\right]\) \(A+C\)

For the following exercises, find the determinant. \(\left|\begin{array}{ll}-8 & 4 \\ -1 & 5\end{array}\right|\)

Determine whether the given ordered pair is a solution to the system of equations. $$ \begin{array}{l} 3 x+7 y=1 \\ 2 x+4 y=0 \text { and }(2,3) \end{array} $$