Question

Solve for $x$ and $y:x-4y-14=0,5x-y-13=0$

Answer 1

$x-4y=14$ ....$\left(1\right)$

$5x-y=13$ ....$\left(2\right)$

By the method of substitution,

Substituting $x=4y+14$ from $\left(1\right)$ in eqn$\left(2\right)$ we get

$5x-y=13$

$\Rightarrow 5(4y+14)-y=13$

$\Rightarrow 20y+60-y=13$

$\Rightarrow 19y=13-60=-47$

$\therefore y=\frac{-47}{19}$

Put $y=\frac{-47}{19}$ in $\left(1\right)$ we get

$x-4y=14\Rightarrow x-4\times \frac{-47}{19}=14$

$\Rightarrow x+\frac{188}{14}=14$

$\Rightarrow x=14-\frac{188}{14}=\frac{196-188}{14}=\frac{8}{14}=\frac{4}{7}$

$\therefore x=\frac{4}{7},y=\frac{-47}{19}$