Question

Solve : $\frac{9}{x}-\frac{4}{y}=8$ and $\frac{13}{x}+\frac{7}{y}=101$

• A. $x=\frac{1}{7}y=\frac{1}{6}$
• B. $x=\frac{3}{4}y=\frac{1}{6}$
• C. $x=\frac{1}{4}y=\frac{1}{7}$
• D. $x=\frac{2}{7}y=\frac{1}{7}$

Answer 1

The correct option is C $x=\frac{1}{4}y=\frac{1}{7}$

Let $\frac{1}{x}=a$ and $\frac{1}{y}=b$

$\frac{9}{x}-\frac{4}{y}=8$ ......(i)
$\Rightarrow 9a-4b=8$ .....(ii)

$\frac{13}{x}+\frac{7}{y}=101$ ......(iii)

$\Rightarrow 13a+7b=101$ .....(iv)
Multipliying equation (ii) by $7$ and (iv) by $4$, we get
$63a-28b=56$
$52a+28b=404$

$115a=460$
$\Rightarrow a=\frac{460}{115}$

$\Rightarrow a=4$
Putting the value in (ii), we get
$9a-4b=8$
$\Rightarrow 9\times 4-4b=8$
$\Rightarrow -4b=8-36$
$\Rightarrow -4b=-28$
$\Rightarrow b=7$
Now, resubstituting the value, we get
$a=\frac{1}{x}=4$ $\Rightarrow x=\frac{1}{4}$
Again, $b=\frac{1}{y}=7$ $\Rightarrow y=\frac{1}{7}$