Question

Solve the simultaneous equation x + y = 2 and 4y² - x²= 11​

Answer 1

The solution sets are (
`(1)/(3),(5)/(3)`) and (5,-3)

Step-by-step explanation:

We are given two equations and we are supposed to solve these two equations and find their solutions.

x + y = 2

4
`y^(2)-x^(2)=11`

Substitute the first equation in the second and make it a quadratic equation in one variable.

4
`y^(2)-(2-y)^(2)= 11`

4
`y^(2)-(y^(2)-4y+4)=11`

`3y^(2)+4y-4=11`

`3y^(2)+4y-15=`

`3y^(2)+9y-5y-15=0`

(3y-5)(y+3) = 0

y =
`(5)/(3)` or y = -3

x =
`(1)/(3)` or x = 5

The solution sets are (
`(1)/(3),(5)/(3)`) and (5,-3)