Question

Determine the value of $(x+y)$ if $\left[\begin{array}{cc}2x+y& 4x\\ 5x-7& 4x\end{array}\right]=\left[\begin{array}{cc}7& 7y-12\\ y& x+6\end{array}\right]$

Answer 1

$\left[\begin{array}{cc}2x+y& 4x\\ 5x-7& 4x\end{array}\right]=\left[\begin{array}{cc}7& 7y-12\\ y& x+6\end{array}\right]$

Comparing the corresponding rows and columns,

$4x=x+6$

$\Rightarrow 4x-x=6$

$\Rightarrow 3x=6$ or $x=\frac{6}{3}=2$

Again,$5x-7=y$

$\Rightarrow 5\times 2-7=y$ since $x=2$

$\therefore y=10-7=3$

Hence $x=2,y=3$