Question

Solve the following simultaneous equation by using an algebraic method (either substitution or elimination)

2x + 3y=-4
4x-y=11

Answer 1

(
`(29)/(14)`, -
`(19)/(7)`)

Explanation:

given the 2 equations

2x + 3y = - 4 → (1)

4x - y = 11 → (2)

Rearrange (2) expressing y in terms of x, that is

y = 4x - 11 → (3)

Substitute y = 4x - 11 into (1)

2x + 3(4x - 11) = - 4

2x + 12x - 33 = - 4

14x - 33 = - 4 ( add 33 to both sides )

14x = 29 ( divide both sides by 14 )

x =
`(29)/(14)`

Substitute this value into (3) for corresponding value of y

y = (4 ×
`(29)/(14)`) - 11 =
`(116)/(14)` -
`(154)/(14)` = -
`(38)/(14)` = -
`(19)/(7)`

solution is (
`(29)/(14)`, -
`(19)/(7)`)