Question

Solve

$\frac{1}{5}(x-2)=\frac{1}{4}(1-y)$
$26x+3y+4=0$

Answer 1

$\frac{1}{5}\left(x-2\right)=\frac{1}{4}\left(1-y\right)$

$\Rightarrow 4\left(x-2\right)=5\left(1-y\right)$

$\Rightarrow 4x-8=5-5y$

$\Rightarrow 4x+5y-13=0.....\left(1\right)$

$26x+3y+4=0......\left(2\right)$

Multiplying $\left(1\right)$ by $\left(3\right)$ and $\left(2\right)$ by $5$ we get

$12x+15y-39=0......\left(3\right)$

$130x+15y+20=0......\left(4\right)$

Subtracting $\left(3\right)$ from $\left(4\right)$ , we get

$\left(130x+15y+20\right)-\left(12x+15y-39\right)=0$

$\Rightarrow 118x+59=0$

$\Rightarrow x=-\frac{59}{118}=-\frac{1}{2}$

putting $x=-\frac{1}{2}$ in $\left(1\right)$

$4\times -\frac{1}{2}+5y=13$

$\Rightarrow 5y-2=13$

$\Rightarrow 5y=15$

$\Rightarrow y=3$

So, $x=-\frac{1}{2}$ , $y=3$