Chapter I : Linear Equations in two variables in two variables

Example 18. The sum of the munerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

Solution: - Let numerator be x and denominator be y

A/Q x + y = 2y - 3

or, x - y + 3 = 0 -------------(1)

and x - 1 = 1/2(y - 1)

or, 2x - y - 1 = 0 ---- -----(2)

Subtracting equation (1) form (2) we get

x = 4

From (1) 4 - y + 3 = 0

y = 7

Fraction = x/y = 4/7