Question

Find '$x+y$' for the following simultaneous equations : $x+2y=2$ and $2x+y=7$.

Answer 1

Let $x+2y=2$ ...(1)
and $2x+y=7$ ...(2)
From equation (2), find the value of $x$ in terms of $y$
$x=\frac{7-y}{2}$ ...(3)
Substituting $x=\frac{7-y}{2}$ in equation (1), we get
$\Rightarrow$ $\left(\frac{7-y}{2}\right)+2y=2$
$\Rightarrow \frac{7}{2}-\frac{y}{2}+2y=2$
$\Rightarrow 2y-\frac{y}{2}=2-\frac{7}{2}$
$\Rightarrow \frac{3y}{2}=\frac{-3}{2}$
$\Rightarrow y=-1$
Substituting $y=-1$ in equation (3),
$x=\frac{7-(-1)}{2}$
$\Rightarrow x=4$
Therefore the value of $x+y$ is $4+(-1)=3$.