Question

Solve the following system by elimination method:
$3x+2y=1$, $2x+3y=4$

Answer 1

Given equations are

$3x+2y=1$ ....(1)

and $2x+3y=4$ ....(2)

Multiply equation (1) by $3$ and equation (2) by $2$, we get

$9x+6y=3$ ....(3)

and $4x+6y=8$ .... (4)

Subtract both the equations to eliminate $y$, we get

$5x=-5$

$\Rightarrow x=-1$

Substitute this value in equation (1),

$3(-1)+2y=1$

$\Rightarrow -3+2y=1$

$\Rightarrow 2y=4$

$\Rightarrow y=2$

Therefore, the solution is $x=-1,y=2$.