Question

Solve the following pair of equations :

$\frac{5y}{2}-\frac{x}{3}=8$
$\frac{y}{2}+\frac{5x}{3}=12$

• A. $x=2;y=7$
• B. $x=4;y=3$
• C. $x=6;y=4$
• D. $x=7;y=3$

Answer 1

The correct option is C $x=6;y=4$

On simplifying $\frac{5y}{2}-\frac{x}{3}=8$, we get $15y-2x=48$ ---- (1)
On simplifying $\frac{y}{2}+\frac{5x}{3}=12$, we get $3y+10x=72$ ---- (2)
Multiplying equation $\left(1\right)$ with $5$ we get, $75y-10x=240$ ----- equation $\left(3\right)$
Adding equation $\left(3\right)$ to $\left(2\right)$, we get

$78y=312=>y=4$
Substituting $y=4$ in the equation $\left(2\right)$, we get

$3\left(4\right)+10x=72=>x=6$