Answer
$ a=2 \\ z=-3\\ k=1\\ m=8$
Work Step by Step
Two matrices are equal when they tare of the same size and their corresponding elements are equal to each other
First, we will find the sum of two matrices of the same size on the left side of the given equality.
$\begin{bmatrix} a+2&3z+1&5m \\8k &0&3\end{bmatrix} + \begin{bmatrix} 3a&2z&5m\\2k&5&6\end{bmatrix} =\begin{bmatrix} 4a+2 &5z+1&10m \\10k&5&9\end{bmatrix} $
Thus, the given equation is equivalent to:
$\begin{bmatrix} 4a+2 &5z+1&10m \\10k&5&9\end{bmatrix} =\begin{bmatrix}10 &-14 &80 \\10&5&9\end{bmatrix} $
Since the two matrices are equal to each other, equate each pair of corresponding elements that contain a variable to obtain:
\begin{align*}
4a+2&=10\\
4a&=8\\
a&=\frac{8}{4}\\
a&=2\\
\\\\
5z+1&=-14\\
5z&=-15\\
z&=\frac{-15}{5}\\
z&=-3\\
\\\\
10k&=10\\
k&=\frac{10}{10}\\
k&=1\\
\\\\
10m&=80\\
m&=\frac{80}{10}\\
m&=8
\end{align*}
