Question

Find the value of $x+y$ if:

$2\left[\begin{array}{cc}x& 7\\ 9& y-5\end{array}\right]+\left[\begin{array}{cc}6& -7\\ 4& 5\end{array}\right]=\left[\begin{array}{cc}10& 7\\ 22& 15\end{array}\right]$.

Answer 1

$2\left[\begin{array}{cc}x& 7\\ 9& y-5\end{array}\right]+\left[\begin{array}{cc}6& -7\\ 4& 5\end{array}\right]=\left[\begin{array}{cc}10& 7\\ 22& 15\end{array}\right]$

$\left[\begin{array}{cc}2x+6& 14-7\\ 18+4& 2(y-5)+5\end{array}\right]=\left[\begin{array}{cc}10& 7\\ 22& 15\end{array}\right]$

The matrix equation is true element-wise.

For the element in 1st row and 1st column:

$2x+6=10\Rightarrow x=2$

For the element in 2nd row and 2nd column:

$2(y-5)+5=15\Rightarrow y=10$

$x+y=10+2=12$