Question

The solution of the pair of linear equations $2y+7x=-5$ and $5y-7x=12$ is

• A. $(1,1)$
• B. $(1,-1)$
• C. $(-1,-1)$
• D. $(-1,1)$

Answer 1

The correct option is D $(-1,1)$

Given equations :
$2y+7x=-5\dots \left(1\right)$
$5y-7x=12\dots \left(2\right)$
Adding equation $1$ and $2$
$2y+7x=-5\dots \left(1\right)$
$\underset{–}{+5y-7x=12}\dots \left(2\right)$
$7y+0=7$

We get,
$7y=7$
$y=1$
Plugging $y=1$ into equation $1$
$2\times 1+7x=-5$
$7x=-7$
$x=-1$
Answer: $(x,y)=(-1,1)$