Question

x − 2y = 4
−3x + 5y = −7

Answer 1

$$\begin{gathered} \mathrm{Given}:x-2y=4 \\ -3x+5y=-7 \\ \mathrm{Using}\mathrm{the}\mathrm{properties}\mathrm{of}\mathrm{determinants},\mathrm{we}\mathrm{get} \\ \mathrm{D}=\left|1-2 \\ -35\right|=5-6=-1\ne 0 \\ {\mathrm{D}}_1=\left|4-2 \\ -75\right|=20-14=6 \\ {\mathrm{D}}_2=\left|14 \\ -3-7\right|=-7+12=5 \\ \mathrm{Using}\mathrm{Cra}\mathrm{mer}\text{'}\mathrm{s}\mathrm{Rule},\mathrm{we}\mathrm{get} \\ \mathrm{x}=\frac{{\mathrm{D}}_1}{\mathrm{D}}=\frac{6}{-1}=-6 \\ \mathrm{y}=\frac{{\mathrm{D}}_2}{\mathrm{D}}=\frac{5}{-1}=-5 \\ \therefore \mathrm{x}=-6\mathrm{and}\mathrm{y}=-5 \end{gathered}$$