If 4x + 6y = 130 and 2x/3y = 4/9, then y - x =?

Question: If 4x + 6y = 130 and 2x/3y = 4/9, then y - x =?

Solution:
here, 2x/3y = 4/9
⇒ x/y = (3/2) × (4/9)
⇒ x/y = 2/3
⇒ x = 2y/3

Given,
4x + 6y = 130
⇒ {4 × (2y/3)} + 6y = 130 [putting value of x]
⇒ (8y/3) + 6y = 130
⇒ (8y + 18y)/3 = 130
⇒ 26y = 390
⇒ y = 15

∴ x= 2y/3
= (2 × 15)/3 = 10

So, y - x = 15 - 10 = 5