Question

Solve the following systems of equations by using the method of substitution:
$\frac{2x}{a}+\frac{y}{b}=2$

$\frac{x}{a}-\frac{y}{b}=4$

Answer 1

$\frac{2}{a}x+\frac{1}{b}y=2$ .......$\left(1\right)$

$\frac{1}{a}x-\frac{1}{b}y=4$ .......$\left(2\right)$

Equation $\left(1\right)+\left(2\right)\Rightarrow \frac{2}{a}x+\frac{1}{a}x=2+4$

$\Rightarrow \frac{3}{a}x=6$

$\Rightarrow x=2a$

Put $x=2a$ in $\left(1\right)$ we get

$\frac{2}{a}\times 2a+\frac{1}{b}y=2$

$4+\frac{1}{b}y=2$

$\frac{1}{b}y=2-4=-2$

$\therefore y=-2b$

Hence $x=2a,y=-2b$