Answer
$(\frac{1}{5}, \frac{9}{5})$
Work Step by Step
Step 1. Define the following matrices based on the given system of equations:
$\begin{array} \\D=\\ \end{array}
\begin{bmatrix} 2&7\\ 6&16\end{bmatrix},
\begin{array} \\D_x=\\ \end{array}
\begin{bmatrix}13&7\\ 30&16 \end{bmatrix},
\begin{array} \\D_y=\\ \end{array}
\begin{bmatrix}2&13\\ 6&30 \end{bmatrix},$
Step 2. Calculate the determinants of the above matrices:
$|D|=2\times16-7\times6=-10$, $|D_x|=13\times16-7\times30=-2$, and $|D_y|=2\times30-13\times6=-18$
Step 3. Use the Cramer's Rule:
$x=\frac{|D_x|}{|D|}=\frac{1}{5}$, $y=\frac{|D_y|}{|D|}=\frac{9}{5}$
Step 4. Conclusion: the solution to the system is $(\frac{1}{5}, \frac{9}{5})$
