Question

Solve the following system by evaluating proportional value of the variables:
$2x+5y=-3$, $5x+2y=-18$

Answer 1

Given equations are

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

and $5x+2y=-18$ ....(2)

Multiply equation (1) by $2$ and equation (2) by $5$,

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

and $25x+10y=-90$ ....(4)

Subtract equations (3) and $4$,

$21x=-84$

$\Rightarrow x=-4$

Put this value in equation (1), we get

$2(-4)+5y=-3$

$\Rightarrow -8+5y=-3$

$\Rightarrow 5y=5$

$\Rightarrow y=1$

Therefore, solution is $x=-4,y=1$.