If there are any similar questions, please link them in the comments. I'm just a little confused as to how you get the answers (which are below).
Find the values of $a$, $b$, $c$, and $d$ in the matrix equation below.
$$\begin{bmatrix}a&b\\c&d\end{bmatrix}+5\begin{bmatrix}-5&-6\\7&x\end{bmatrix}^T=\begin{bmatrix}-1&-3\\-3&6\end{bmatrix}$$
$$\begin{align}a&=24\\b&=-38\\c&=27\\d&=6-5x\end{align}$$
Best Answer
$$\begin{bmatrix}-5&-6\\7 & x\end{bmatrix}^T=\begin{bmatrix}-5 & 7 \\ -6 & x\end{bmatrix}$$ Therefore, $$\begin{bmatrix}a&b\\c&d\end{bmatrix}+5\begin{bmatrix}-5 & 7 \\ -6 & x\end{bmatrix}=\begin{bmatrix}a-25&b+35\\c-30 & d+5x\end{bmatrix}=\begin{bmatrix}-1 & -3 \\ -3 &6\end{bmatrix}.$$