Question

Solve the following system of equation by Substitution method.
$x+y=7$
$3x-2y=11$

Answer 1

Given the system of equation
$x+y=\mathrm{7.......}\left(i\right)$
$3x-2y=\mathrm{11....}\left(ii\right)$
From equation $\left(i\right)$
$x+y=7$
$x=7-y.......\left(iii\right)$
Putting the value of $x$ from $\left(iii\right)$ in equation $\left(ii\right)$
$3(7-y)-2y=11$
$\Rightarrow$ $21-3y-2y=11$
$\Rightarrow$ $21-5y=11$
$\Rightarrow$ $-5y=11-21$
$\Rightarrow$ $y=\frac{10}{5}=2$
$\Rightarrow$ $y=\mathrm{2........}\left(iv\right)$
Putting the value of $y$ from $\left(iv\right)$ in equation$\left(iii\right)$
$\Rightarrow$ $x=7-2$
$\Rightarrow$ $x=5$
$\Rightarrow$ $x=5$ and $y=2$