Question

Solve the following system by elimination method:
$2x+3y=13$, $4x+y=11$

Answer 1

Given equations are

$2x+3y=13....\left(1\right)$

$4x+y=11.....\left(2\right)$

multiply the equation $\left(2\right)$ by $3$, we get

$\Rightarrow 12x+3y=33.....\left(3\right)$

Subtract equation $\left(1\right)$ from $\left(3\right)$ to eliminate $y$, we get

$12x+3y=33$

$2x+3y=13$

$-$ $-$ $-$

$\overline{10x=20}$

$\Rightarrow x=2$

Put this value in equation $\left(1\right)$, we get

$\Rightarrow 2\left(2\right)+3y=13$

$\Rightarrow 4+3y=13$

$\Rightarrow 3y=9$

$\Rightarrow y=3$

$\therefore$ the solution is $x=2,y=3$.