4y-x=5+2y; 3x+7y=24 solve systen by using substitution

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