Question - Matrix Equation Solution

Let A = \begin{pmatrix} 0 & 1 \\ y & 5 \end{pmatrix}, B = \begin{pmatrix} 4 & -1 \\ 6 & x \end{pmatrix}, C = \begin{pmatrix} 4 & 0 \\ x & 7 \end{pmatrix}.

Then, we have:

A + B = C.

Thus, we can write:

\begin{pmatrix} 0 + 4 & 1 - 1 \\ y + 6 & 5 + x \end{pmatrix} = \begin{pmatrix} 4 & 0 \\ x & 7 \end{pmatrix}.

From this, we can derive the equations:

0 + 4 = 4,

1 - 1 = 0,

y + 6 = x,

5 + x = 7.

Solve the last equation for x:

x = 7 - 5 = 2.

Then substitute x back into the third equation:

y + 6 = 2.

y = 2 - 6 = -4.

The values of y and x are:

x = 2,

y = -4.