Answer
$x=\begin{bmatrix}
-48\\
14
\end{bmatrix}$
Work Step by Step
Write the system in the matrix form:
$\begin{bmatrix}
6 & 20\\
2& 7
\end{bmatrix}.\begin{bmatrix}
x_1\\
x_2
\end{bmatrix}=\begin{bmatrix}
-8\\
2
\end{bmatrix}$
Find the inverse for matrix $A=\begin{bmatrix}
6 & 20\\
2& 7
\end{bmatrix}$:
$\begin{bmatrix}
6 & 20 | 1 & 0\\
2& 7 | 0 & 1
\end{bmatrix} \approx^1 \begin{bmatrix}
1 &\frac{10}{3} | \frac{1}{6} & 0\\
2& 7 | 0 & 1
\end{bmatrix} \approx^2 \begin{bmatrix}
1 &\frac{10}{3} | \frac{1}{6} & 0\\
0& \frac{1}{3} | -\frac{1}{3} & 1
\end{bmatrix} \approx^3 \begin{bmatrix}
1 &\frac{10}{3} | \frac{1}{6} & 0\\
0& 1 | -1 & 3
\end{bmatrix} \approx^4 \begin{bmatrix}
1 &0 | \frac{21}{6} & -10\\
0& 1 | -1 & 3
\end{bmatrix}$
Hence, $A^{-1}=\begin{bmatrix}
\frac{7}{2} & -10\\
-1 & 3
\end{bmatrix}$
Using $x=A^{-1}b$ to find x:
$X=\begin{bmatrix}
\frac{7}{2} & -10\\
-1 & 3
\end{bmatrix}.\begin{bmatrix}
-8\\
2
\end{bmatrix}=\begin{bmatrix}
-48\\
14
\end{bmatrix}$
