Question

Solve the following simultaneous equations: $\frac{x}{3}+5y=13$ and $2x+\frac{y}{2}=19$

• A. $x=2$, $y=9$
• B. $x=-2$, $y=-9$
• C. $x=-2$, $y=9$
• D. $x=9$, $y=2$

Answer 1

The correct option is D $x=9$, $y=2$

$\frac{x}{3}+5y=13⟹x+15y=\mathrm{39...}\left(1\right)$
$2x+\frac{y}{2}=19⟹4x+y=\mathrm{38...}\left(2\right)$
Multiplying (1) by 4, we have $4x+60y=\mathrm{156...}\left(3\right)$
(3)-(2)$⟹59y=118⟹y=2$
Substituting this value of $y$ in (1), we have $x+15\left(2\right)=39⟹x=39-30=9$
Thus, $x=9andy=2$