Question

Solve:$2x+y=3$ and $x-2y=1$

Answer 1

$2x+y=3\Rightarrow y=3-2x$

Substituting $y=3-2x$ in $x-2y=1$ we get

$x-2(3-2x)=1$

$\Rightarrow x-6+4x=1$

$\Rightarrow 5x=1+6=7$

$\Rightarrow x=\frac{7}{5}$

Put $x=\frac{7}{5}$ in $x-2y=1$ we get

$\Rightarrow \frac{7}{5}-2y=1$

$\Rightarrow -2y=1-\frac{7}{5}=\frac{5-7}{5}=\frac{-2}{5}$

$\Rightarrow y=\frac{1}{5}$

$\therefore x=\frac{7}{5},y=\frac{1}{5}$