Answer
$(65,154)$
Work Step by Step
Step 1. Define the following mor $(65,154)$atrices:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 12&-5\\ 5&-2\end{bmatrix},
\begin{array} \\X=\\ \end{array}
\begin{bmatrix} x\\ y\end{bmatrix},
\begin{array} \\B=\\ \end{array}
\begin{bmatrix} 10\\17\end{bmatrix}$
Step 2. Rewrite the original system of equations as
$AX=B$, thus $A^{-1}AX=X=A^{-1}B$
Step 3. Find the inverse $A^{-1}$ using the formula given in section 10.5:
$\begin{array} \\A^{-1}=\frac{1}{-24+25}\\ \end{array}
\begin{bmatrix} -2&5\\ -5&12\end{bmatrix}
=\begin{bmatrix} -2&5\\ -5&12\end{bmatrix}$
Step 4. Find the solutions as:
$\begin{array} \\A^{-1}B=\\ \end{array}
\begin{bmatrix} -2&5\\ -5&12\end{bmatrix}
\begin{bmatrix} 10\\17\end{bmatrix}
=\begin{bmatrix} -20+85\\-50+204\end{bmatrix}
=\begin{bmatrix} 65\\154\end{bmatrix}$
or $(65,154)$
