Question

Solve for x and y:

`(x + y - 8)/2 = (x + 2y - 14)/3 = (3x + y - 12)/11`

Answer 1

The given equations are:

`(x + y - 8)/2 = (x + 2y - 14)/3 = (3x + y - 12)/11`

i.e.,`(x + y - 8)/2 = (3x + y - 12)/11`

By cross multiplication, we get:

11x + 11y – 88 = 6x + 2y – 24

⇒ 11x – 6x + 11y – 2y = –24 + 88

⇒ 5x + 9y = 64   ...(i)

And `(x + 2y - 14)/3 = (3x + y - 12)/11`

⇒ 11x + 22y – 154 = 9x + 3y – 36

⇒ 11x – 9x + 22y – 3y = –36 + 154

⇒ 2x + 19y = 118   ...(ii)

On multiplying (i) by 19 and (ii) by 9, we get:

95x + 171y = 1216   ...(iii)

18x + 171y = 1062   ...(iv)

On subtracting (iv) from (iii), we get:

77x = 154

⇒ x = 2

On substituting x = 2 in (i), we get:

10 + 9y = 64

⇒ 9y = (64 – 10)

⇒ 9y = 54

⇒ y = 6

Hence, the solution is x = 2 and y = 6.