Solve the following for x and y:

Solution:

Here,

$\left[\begin{array}{cc}3 & -4 \\ 9 & 2\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}10 \\ 2\end{array}\right]$

$\Rightarrow\left[\begin{array}{l}3 x-4 y \\ 9 x-2 y\end{array}\right]=\left[\begin{array}{c}10 \\ 2\end{array}\right]$

$\Rightarrow 3 x-4 y=10 \quad \ldots(1)$

$9 x+2 y=2 \quad \ldots(2)$

Solving both the equations, we get

$x=\frac{14}{21}$

$=\frac{2}{3}$

Substituting the value of $x$ in eq. (1), we get

$3 \times \frac{2}{3}-4 y=10$

$\Rightarrow 2-4 y=10$

$\Rightarrow 4 y=-8$

$\Rightarrow y=-2$

$\therefore x=\frac{2}{3}$ and $y=-2$