4y - x = 5 + 2y ..... (1)
3x + 7y = 24 ..... (2)
by grouping like terms in (1)
4y - x = 5 + 2y
4y - 2y - x = 5
-x + 2y = 5 ..... (1a)
by multiplying (1a) through by -3
(-3)(-x) + 2(-3)y = 5(-3)
3x - 6y = -15 ..... (1b)
by subtracting 1a from 2
3x -3x + 7y - (-6y) = 24 - (-15)
13y = 39
⇒ y = 3
by substituting y=3 into (2)
3x + 7(3) = 24
3x = 24 - 21
3x = 3
⇒ x = 1
∴ solution to the system is x=1 when y = 3