Question

Use elimination method for solving the following equations:
$2x+y=7$, $2x-3y=3$

Answer 1

Given equations are

$2x+y=7$ ....(1)

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

Multiply equation (1) by $3$,

$6x+3y=21$ ....(3)

Add equations (2) and (3) to eliminate $y$, we get

$8x=24$

$\Rightarrow x=3$

Substitute this value of $x$ in equation (1),

$2\left(3\right)+y=7$

$\Rightarrow 6+y=7$

$\Rightarrow y=1$

Therefore, solution is $x=3,y=1$.