Question

Solve the following pair of simultaneous equations.
$\frac{x}{3}+\frac{y}{12}=\frac{7}{2}$ and $\frac{x}{6}-\frac{y}{8}=\frac{6}{8}$

• A. $x=9$ and $y=6$
• B. $x=4$ and $y=7$
• C. $x=16$ and $y=2$
• D. $x=12$ and $y=3$

Answer 1

The correct option is A $x=9$ and $y=6$

$\frac{x}{3}+\frac{y}{12}=\frac{7}{2}$
$\frac{4x+y}{12}=\frac{7}{2}$
$4x+y=\mathrm{42.....}\left(i\right)$
$\frac{x}{6}-\frac{y}{8}=\frac{6}{8}$
$\frac{4x-3y}{24}=\frac{6}{8}$
$4x-3y=\mathrm{18.......}\left(ii\right)$
$4x+y=42$
$4x-3y=18$
-------------------
$4y=24$
$y=6$
Substitute $y=6$ in equation $\left(i\right)$
$4x+6=42$
$\Rightarrow$ $4x=36$
Hence, $x=9$ and $y=6$