Question

If $2x-y=32$ and $5x+3y=14$, then $xy=$

• A. $35$
• B. $-40$
• C. $75$
• D. $100$
• E. $-120$

Answer 1

Answer: (E)

$-120$

Let $2x-y=32...\left(1\right)$
and $5x+3y=14...\left(2\right)$
Multiplying equation $\left(1\right)$ with $3$, we get
$6x-3y=96...\left(3\right)$
Adding equations $\left(2\right)$ and $\left(3\right)$, we get
$11x=110$
$\Rightarrow x=10$
Substituting in $\left(1\right)$, we get
$20-y=32$
$\Rightarrow y=-12$
Thus, $xy=10\times (-12)=-120$