Solving system of equations where variables are matrices

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So I have a work sheet and the question was

"Solve the system of matrix equations for X and Y, that is, find X and Y matrices of size 4 x 3 satisfying the relations"

$$2X-Y = \begin{bmatrix}-12&-7&-4\\ -5&8&-7\\ 4&3&-1\\ 4&-6&-11\end{bmatrix}$$

And

$$X+3Y = \begin{bmatrix}40&25&16\\17&-27&24\\-15&-12&2\\-15&19&36\end{bmatrix}$$

So I don't quite understand what the want me to do I tried to solve the matrix using the Gaussian elimination but the system has no solution

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Hint:

Suppose you are dealing with simultaneous equation:

$$2x-y=a$$

$$x+3y=b$$

where $a$ and $b$ are just real numbers, $x, y$ are in the real number as well. what would you have done to express $x$ and $y$ in terms of $a$ and $b$.

After you think through the above, then try to check can you do the same thing when you deal with matrices.