Question

3x + ay = 4
2x + ay = 2, a ≠ 0

Answer 1

$$\begin{gathered} \mathrm{Given}:3x+ay=4 \\ 2x+ay=2 \\ \mathrm{Using}\mathrm{Cramer}\text{'}\mathrm{s}\mathrm{rule},\mathrm{we}\mathrm{get} \\ \mathrm{D}=\left|3\mathrm{a} \\ 2\mathrm{a}\right|=3\mathrm{a}-2\mathrm{a}=\mathrm{a} \\ {\mathrm{D}}_1=\left|4\mathrm{a} \\ 2\mathrm{a}\right|=4\mathrm{a}-2\mathrm{a}=2\mathrm{a} \\ {\mathrm{D}}_2=\left|34 \\ 22\right|=6-8=-2 \\ \mathrm{Now}, \\ \mathrm{x}=\frac{{\mathrm{D}}_1}{\mathrm{D}}=\frac{2\mathrm{a}}{\mathrm{a}}=2 \\ \mathrm{y}=\frac{{\mathrm{D}}_2}{\mathrm{D}}=\frac{-2}{\mathrm{a}}=-\frac{2}{\mathrm{a}} \\ \therefore \mathrm{x}=2\mathrm{and}\mathrm{y}=-\frac{2}{\mathrm{a}} \end{gathered}$$