Question

Solve: $x+2y=3,2x-y=5$

Answer 1

$x+2y=3$

$\Rightarrow x=3-2y$

Substituting $x=3-2y$ in $2x-y=5$,

$\begin{array}{cc}2\left(3-2y\right)-y& =5\\ 6-4y-y& =5\\ -5y& =5-6\\ -5y& =-1\\ y& =\frac{1}{5}\end{array}$

Substitute $y=\frac{1}{5}$ in $x=3-2y$ we get,

$\begin{array}{cc}x& =3-2\times \frac{1}{5}\\ & =\frac{15-2}{5}\\ & =\frac{13}{5}\end{array}$

$\therefore x=\frac{13}{5},y=\frac{1}{5}$