Question

Given that $2x-5y=13$ and $2x+y=-5$, find the value of $y$.

• A. $-3$
• B. $-1$
• C. $1$
• D. $14$

Answer 1

The correct option is A $-3$

$2x-5y=13$ .............. (1)

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

Multiply (2) by $5$, we get

$2x\times 5+y\times 5=-5\times 5$

$\Rightarrow 10x+5y=-25$ .............. (3)

Add (3) with (1) we get

$(10x+5y)+(2x-5y)=-25+13$

$\Rightarrow 10x+5y+2x-5y=-12$

$\Rightarrow 12x=-12$

$\Rightarrow x=-1$

Put the value $x=-1$ in (2) we get

$2(-1)-5y=13\Rightarrow -5y=13+5\Rightarrow y=-3$

Then, $x=-1$ and $y=-3$