Answer
$X=\begin{bmatrix}
-\frac{1}{4} & \frac{5}{2}\\
\frac{11}{2} &5
\end{bmatrix}$
Work Step by Step
Multiply the inverse of the matrix on the left by the matrix on the right:
$X=\begin{bmatrix}
-2& 1\\
4 & 0
\end{bmatrix}^{-1}\begin{bmatrix}
6& 0\\
-1 & 0
\end{bmatrix}\\=\frac{1}{0-4}\begin{bmatrix}
0 &-1\\
-4 & -2
\end{bmatrix}\begin{bmatrix}
6& 0\\
-1 & 0
\end{bmatrix}\\=-\frac{1}{4}\begin{bmatrix}
(0)(6)+(-1)(-1)& (0)(0)+(-1)(10)\\
(6)(-4)+(-2)(-1) & (-4)(0)+(10)(-2)
\end{bmatrix}\\=\frac{1}{8}\begin{bmatrix}
6-30 & -10+5\\
-6+6 & 10-1
\end{bmatrix}\\=\frac{-1}{4}\begin{bmatrix}
1& -10\\
-22& -20
\end{bmatrix}\\=\begin{bmatrix}
-\frac{1}{4} & \frac{5}{2}\\
\frac{11}{2} &5
\end{bmatrix}$
