Answer
$$x_1=10,\quad x_2= -12.$$
Work Step by Step
We have the system
$$\left[ \begin {array}{ccc} 5&4\\ -1& 1 \end {array} \right]
\left[\begin{array}{rrr}{x_1}\\ {x_2} \end{array}\right]=\left[\begin{array}{rrr}{2} \\ {-22} \end{array}\right].$$
The coefficients matrix $A= \left[ \begin {array}{ccc} 5&4\\ -1& 1 \end {array} \right]
$ has the inverse
$$A^{-1}=\left[ \begin {array}{cc} \frac{1}{9}&-\frac{4}{9}\\ \frac{1}{9}&\frac{5}{9}
\end {array} \right]
.
$$
The system has the solution
$$\left[\begin{array}{rrr}{x_1}\\ {x_2} \end{array}\right]=\left[ \begin {array}{cc} \frac{1}{9}&-\frac{4}{9}\\ \frac{1}{9}&\frac{5}{9}
\end {array} \right]\left[\begin{array}{rrr}{2} \\ {-22} \end{array}\right]=\left[ \begin {array}{c} {10}\\ -12
\end {array} \right]
.$$
That is
$$x_1=10,\quad x_2= -12.$$
