Question

If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.

Answer 1

10 y = 7x - 4

- 7x + 10y = - 4

- (7x - 10y) = 4

7x - 10y = 4                ...(1)

12x + 18y = 1             ...(2)

Multiplying equation no. (1) by 12 and (2) by 7.

84x - 120y = 48               ....(3)

84x + 126y = 7                     ....(4)

Substract equation (3) and (4)

  84x - 120y = 48
  84x + 126y = 7 
(-)     (-)           (-)
 - 246 y = 41

y = `41/(- 246)`

y = - `1/6`

From (1)

7x - 10`(-1/6)` = 4

7x + `5/3` = 4

7x = `4 - 5/3`

7x = `7/3`

x = `7/3 xx 7`

x = `1/3`

∴ 4x + 6y = `4(1/3) + 6(-1/6) = 4/3 - 6/6 = 4/3 - 1 = 1/3`

∴ 8y - x = `8(-1/6) - 1/3 = -4/3 - 1/3 = -5/3`