Solve this

Given: $\quad x-2 y=4$

$-3 x+5 y=-7$

Using the properties of determinants, we get

$\mathrm{D}=\mid \begin{array}{ll}1 & -2\end{array}$

$-3 \quad 5 \quad \mid=5-6=-1 \neq 0$

$\mathrm{D}_{1}=\mid 4 \quad-2$

$-7 \quad 5 \mid=20-14=6$

$\mathrm{D}_{2}=\mid 1 \quad 4$

$-3-7 \mid=-7+12=5$

Using Cramer's Rule, we get

$\mathrm{x}=\frac{\mathrm{D}_{1}}{\mathrm{D}}=\frac{6}{-1}=-6$

$\mathrm{y}=\frac{\mathrm{D}_{2}}{\mathrm{D}}=\frac{5}{-1}=-5$

$\therefore \mathrm{x}=-6$ and $\mathrm{y}=-5$