Question

Solve the simultaneous equation

Answer 1

x =
`-(11)/(5), 3`

y =
`-(8)/(5),1`

Explanation:

3xy - y² = 8 -------(1)

x - 2y = 1 ------(2)

From equation (2),

x = 2y + 1

By substituting the value of x in equation (1),

3y(2y + 1) - y² = 8

6y² + 3y - y² = 8

5y² + 3y - 8 = 0

5y² + 8y - 5y - 8 = 0

y(5y + 8) - 1(5y + 8) = 0

(y - 1)(5y + 8) = 0

y =
`-(8)/(5),1`

From equation (2),

x = 2y + 1

For y =
`-(8)/(5)`,

x =
`-2((8)/(5))+1`

x =
`-(11)/(5)`

For y = 1,

x = 2(1) + 1

x = 3

Therefore, x =
`-(11)/(5), 3`

y =
`-(8)/(5),1`