Answer
$$x=1,\quad y=-5.$$
Work Step by Step
We have the system
$$\left[\begin{array}{rrr}{5} & {4} \\{-1}& {1} \end{array}\right]\left[\begin{array}{rrr}{x}\\ {y} \end{array}\right]=\left[\begin{array}{rrr}{-15} \\ {-6} \end{array}\right].$$
The coefficients matrix $A=\left[\begin{array}{rrr}{5} & {4} \\{-1}& {1} \end{array}\right]$ 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
$$\left[\begin{array}{rrr}{x}\\ {y} \end{array}\right]=\left[ \begin {array}{cc} \frac{1}{9}&-\frac{4}{9}\\ \frac{1}{9}&\frac{5}{9}
\end {array} \right]\left[\begin{array}{rrr}{-15} \\ {-6} \end{array}\right]=\left[ \begin {array}{c} 1\\ -5\end {array}
\right]
.$$
That is
$$x=1,\quad y=-5.$$
