Question

Solve:
$8x+2y=4;x-4y=5$

Answer 1

$8x+2y=4$

$\Rightarrow 4x+y=2$ dividing by $2$

$4x+y=2$ ......$\left(1\right)$

$x-4y=5$ ......$\left(2\right)$

Solving $\left(1\right)$ and $\left(2\right)$ we get

$4\times$eqn$\left(2\right)-1\times$eqn$\left(1\right)$

$\Rightarrow 4x-16y-4x-y=20-2$

$\Rightarrow -17y=18$

$\therefore y=\frac{-18}{17}$

substitute $y=\frac{-18}{17}$ in $\left(1\right)$ we get

$4x-\frac{18}{17}=2$

$\Rightarrow 4x=2+\frac{18}{17}=\frac{34+18}{17}=\frac{52}{17}$

$\therefore x=\frac{52}{17\times 4}=\frac{13}{17}$

Hence $x=\frac{13}{17}$ and $y=\frac{-18}{17}$