Question

Find the value of $x$ and $y$ that satisfy the equation:
$\left[\begin{array}{cc}3& -2\\ 3& 0\\ 2& 4\end{array}\right]\left[\begin{array}{cc}y& y\\ x& x\end{array}\right]=\left[\begin{array}{cc}3& 3\\ 3y& 3y\\ 10& 10\end{array}\right]$

• A. $x=3/2,y=2$
• B. $x=2,y=3/2$
• C. $x=3,y=2$
• D. $x=2,y=3$

Answer 1

The correct option is A $x=3/2,y=2$

$\left[\begin{array}{cc}3& -2\\ 3& 0\\ 2& 4\end{array}\right]\left[\begin{array}{cc}y& y\\ x& x\end{array}\right]=\left[\begin{array}{cc}3& 3\\ 3y& 3y\\ 10& 10\end{array}\right]\Rightarrow \left[\begin{array}{cc}3y-2x& 3y-2x\\ 3y& 3y\\ 2y+4x& 2y+4x\end{array}\right]=\left[\begin{array}{cc}3& 3\\ 3y& 3y\\ 10& 10\end{array}\right]$
$\therefore 3y-2x=3$ and $2y+4x=10$
$\Rightarrow x=\frac{3}{2},y=2$