Answer
$x=-1$ and $y=5$
Work Step by Step
Since two matrices are equal if all their corresponding elements are equal, the given matrix equation, $
\begin{bmatrix}
-3+2x & 2
\\
4 & -7y
\end{bmatrix}
=
\begin{bmatrix}
x-4 & 2
\\
4 & -35
\end{bmatrix}
,$ implies the following equations:
\begin{align*}
-3+2x&=x-4
\\&\text{ and }\\
-7y&=-35
\end{align*}
Using the properties of equality, the equations above are equivalent to
\begin{align*}
-3+3+2x-x&x-x-4+3
\\
2x-x&=-4+3
\\
x&=-1
\\\\&\text{ AND}\\\\
\dfrac{-7y}{-7}&=\dfrac{-35}{-7}
\\\\
y&=5
\end{align*}
Hence, $
x=-1$ and $y=5
.$
