Answer
$(8,-4)$
Work Step by Step
Step 1. Define the following matrices based on the given system of equations:
$\begin{array} \\D=\\ \end{array}
\begin{bmatrix} 12&-11\\ 7&9\end{bmatrix},
\begin{array} \\D_x=\\ \end{array}
\begin{bmatrix} 140&-11\\ 20&9 \end{bmatrix},
\begin{array} \\D_y=\\ \end{array}
\begin{bmatrix} 12&140\\ 7&20 \end{bmatrix}$
Step 2. Calculate the determinants of the above matrices:
$|D|=12\times9+11\times7=185$, $|D_x|=140\times9+11\times20=1480$, and $|D_y|=12\times20-140\times7=-740$
Step 3. Use the Cramer's Rule:
$x=\frac{|D_x|}{|D|}=8$, $y=\frac{|D_y|}{|D|}=-4$
Step 4. Conclusion: the solution to the system is $(8,-4)$
