Question

Solve the following system by evaluating proportional value of the variables:
$3x+2y=4$, $2x-3y=7$

Answer 1

Given equations are

$3x+2y=4$ ....(1)

and $2x-3y=7$ ....(2)

Multiply equation (1) by $3$ and equation (2) by $2$

Therefore, $9x+6y=12$ ....(3)

and $4x-6y=14$ .....(4)

Now add both the equations,we get

$13x=26$

$\Rightarrow x=2$

Put this value of $x$ in equation (1)

$3\left(2\right)+2y=4$

$\Rightarrow 6+2y=4$

$\Rightarrow 2y=-2\Rightarrow y=-1$

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