We are given the matrix equation:

$X + D = E$

where

$D = \begin{pmatrix} -7 & 0 \\ -4 & \end{pmatrix}$ and

$E = \begin{pmatrix} -2 & 1 \\ -3 & \end{pmatrix}$

To solve for $X$, we can isolate $X$ on one side by subtracting $D$ from both sides of the equation:

$X = E - D$

Now, subtract $D$ from $E$ element-wise:

$X = \begin{pmatrix} -2 & 1 \\ -3 & \end{pmatrix} - \begin{pmatrix} -7 & 0 \\ -4 & \end{pmatrix}$

Performing the subtraction:

$X = \begin{pmatrix} -2 - (-7) & 1 - 0 \\ -3 - (-4) & 0 - 0 \end{pmatrix}$

$X = \begin{pmatrix} -2 + 7 & 1 \\ -3 + 4 & 0 \end{pmatrix}$

$X = \begin{pmatrix} 5 & 1 \\ 1 & 0 \end{pmatrix}$

Thus, the solution for $X$ is:

$X = \begin{pmatrix} 5 & 1 \\ 1 & 0 \end{pmatrix}$

Would you like any additional details or clarifications?

Here are some related questions you could explore:

1. What is the inverse of matrix $X$?
2. How can we perform matrix addition or multiplication?
3. What are the properties of matrix subtraction?
4. How does matrix transposition work?
5. How do we find the determinant of a 2x2 matrix?

Tip: When subtracting matrices, ensure that they have the same dimensions; otherwise, the operation cannot be performed.