Question

Write the linear equations in two variables for the given information :
A fraction becomes $\frac{9}{11}$ , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$.

Answer 1

Let fraction is $\frac{x}{y}$

Now according to question
$\frac{x+2}{y+2}=\frac{9}{11}$

Þ 11x + 22 = 9y + 18

Þ 11x – 9y = – 4 …..(i)

and
$\frac{x+3}{y+3}=\frac{5}{6}$
$\Rightarrow 6x+18=5y+15$

Þ 6x – 5y = –3 ….(ii)