Question

Solve the following pair of equations $\frac{x}{8}-\frac{y}{7}=\frac{17}{28};\frac{x}{7}-\frac{y}{8}=1$

• A. $x=5,y=8$
• B. $x=19,y=8$
• C. $x=12,y=8$
• D. $x=14,y=8$

Answer 1

Answer: (D)

$x=14,y=8$

Given, $\frac{x}{8}-\frac{y}{7}=\frac{17}{28};\frac{x}{7}-\frac{y}{8}=1$
Rewriting the given equations, we get
$7x-8y=34$ ...(i)
$8x-7y=56$ ...(ii)
On multiplying (i) by 8 and (ii) by 7, we get
$56x-64y=272$
$\underset{–}{\underset{-}{5}6x\underset{+}{-}49y=\underset{-}{3}92}$
$-15y=-120$
$\therefore y=8$
On putting $y=8$ in (i), we get
$7x-8\left(8\right)=34$
$\Rightarrow 7x=34+64$
$\Rightarrow x=14$
$\therefore x=14,y=8$