Question

Choose the solution(s) of the following system of equations x2 + y2 = 6 x2 – y = 6

Answer 1

(√6,0)

(√5,-1)

(-√6,0)

(-√5,-1)

Explanation:

Edg 2021

Answer 2

`x=√(6), y=0\\ x=-√(6) , y=0\\x=√(5) , y=-1\\x=-√(5) , y=-1`

Or as ordered pairs:
`(√(6) ,0),(-√(6) ,0),(√(5) ,-1),(-√(5) ,-1)`

Explanation

Lets solve our system of equations step by step

`x^2+y^2=6` equation (1)

`x^2-y=6` equation (2)

1. Solve for
`x^2` in equation (2)

`x^2-y=6`

`x^2=6+y` equation (3)

2. Replace equation (3) in equation (1) and solve for
`y`

`x^2+y^2=6`

`6+y+y^2=6`

`y^2+y=0`

`y(y+1)=0`

`y=0` or
`y=-1`

3. Replace the values of
`y` in equation (3) and solve for
`x`

- For
`y=0`

`x^2=6+y`

`x^2=6`

`x=√(6)` or
`x=-√(6)`

- For
`y=-1`

`x^2=6+y`

`x^2=6-1`

`x^2=5`

`x=√(5)` or
`x=-√(5)`

So, the solutions of our system of equation are:

`x=√(6), y=0\\ x=-√(6) , y=0\\x=√(5) , y=-1\\x=-√(5) , y=-1`