Question

Solve the following equation
$2x+\frac{y}{2}-5=0$
$\frac{x}{2}+y=-4$

Answer 1

The given equations are

$2x+\frac{y}{2}-5=0$ .........(1)

$\frac{x}{2}+y=-4$ ...........(2)

Multiple equation (2) by $4$

It becomes $2x+4y=-16$ .........(3)

Subtract (1) from (3)

$2x+4y=-16$

$2x+\frac{y}{2}=5$

$-$ $-$ $-$

$\overline{4y-\frac{y}{2}=-21}$

$\frac{7y}{2}=-21$

$y=\frac{-21\times 2}{7}$

$y=-6$

Put $y=-6$ in (1)

$2x-\frac{6}{2}=5$

$2x-3=5$ $2x=8$

$x=4$

So, $x=4$ and $y=-6$ is the solution of two given equations.