Question

Find the value of $x,y,p$ and $q$ if

$[\begin{array}{c}p+q\\ x+3y\end{array}\begin{array}{c}2x-3y\\ p-2q\end{array}]=[\begin{array}{c}6\\ 3\end{array}\begin{array}{c}9\\ 3\end{array}]$

Answer 1

$\left[\begin{array}{cc}p+q& 2x-3y\\ x+3y& p-2q\end{array}\right]=\left[\begin{array}{cc}6& 9\\ 3& 3\end{array}\right]$

$p+q=6----\left(1\right)$

$p-2q=3---\left(2\right)$

Subtract $2from1$

$3q=3$ $q=1$

$\therefore p=5$

$2x-3y=\mathrm{9.....}\left(3\right)$

$x+3y=\mathrm{3......}\left(4\right)$

Add $3and4$

$3x=12\to x=4$

$\therefore y=\frac{-1}{3}$

$x=4,y=\frac{-1}{3},p=5,q=1$