Question

Solve the following simultaneous equations:

$\frac{2x}{3}+\frac{y}{4}=12;\frac{4x}{3}-\frac{9y}{4}=2$

• A. $x=12,y=5$
• B. $x=15,y=8$
• C. $x=13,y=4$
• D. $x=14,y=9$

Answer 1

Answer: (B)

$x=15,y=8$

Rewriting the given equations after taking LCM,

$8x+3y=144$ ...$\left(1\right)$

$16x-27y=24$ ...$\left(2\right)$

Multiplying $\left(1\right)$ by $2$

$16x+6y=288$ ...$\left(3\right)$

$16x-27y=24$ ...$\left(2\right)$

Subtracting $\left(3\right)$ and $\left(2\right)$,

$33y=264$

$y=8$

Substituting $y=8$ in $\left(1\right)$, we get

$8x+24=144$

$8x=120$

$x=15$

$x=15,y=8$

Option $B$