Question

Solve:$x+2y=7;2x-7y=8$

Answer 1

By the method of substitution,

$x+2y=7$

$\Rightarrow x=7-2y$

We have $2x-7y=8$

$\Rightarrow 2(7-2y)-7y=8$

$\Rightarrow 14-4y-7y=8$

$\Rightarrow -11y=8-14=-6$

$\Rightarrow y=\frac{-6}{-11}=\frac{6}{11}$

Substitute $y=\frac{6}{11}$ in $x=7-2y$ we get

$x=7-2\times \frac{6}{11}=7-\frac{12}{11}=\frac{77-12}{11}=\frac{65}{11}$

$\therefore x=\frac{65}{11}$ and $y=\frac{6}{11}$