Question

Solve the following system of equation by elimination method:
$3x+2y=11,2x+3y=4$

Answer 1

$3x+2y=\mathrm{11........}\left(1\right)$
$2x+3y=\mathrm{4..........}\left(2\right)$
Multiplying equation $\left(1\right)$ by $2$ and equation $\left(2\right)$ by $3$ and subtracting
$\left(6x+4y\right)-\left(6x+9y\right)=22-12$

$\Rightarrow -5y=10$

$\Rightarrow y=-2$

Substitute the value of $y$ in equation $\left(1\right),$
$3x+2\times (-2)=11$
$\Rightarrow$ $3x=11+4=15$
$\Rightarrow$ $x=\frac{15}{3}=5$
$\Rightarrow x=5$

$\therefore$ Solution of system of equations is $x=5,y=-2.$