Question

Solve the following system by elimination method:
$3x+2y=5$, $5x-4y=23$

Answer 1

Given equations are

$3x+2y=5$ ....(1)

and $5x-4y=23$ .....(2)

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

$6x+4y=10$ ....(3)

Now add equations both the equations to eliminate $y$,

$11x=33$

$\Rightarrow x=3$

Put this value in equation (1), we get

$3\left(3\right)+2y=5$

$\Rightarrow 9+2y=5$

$\Rightarrow 2y=5-9$

$\Rightarrow y=-2$

Therefore, the solution is $x=3,y=-2$.