# Choose the solution(s) of the following system of equations: x2 + y2 = 6 and x2 - y = 6

No solution, (√6, 0), (√5, 1), (√5, -1), Infinitely many solutions, (-√6, 0), (-√5, 1), (-√5, -1)

**Solution:**

Given: Linear equations are x^{2} + y^{2} = 6 and x^{2} - y = 6

In order to find solution, we need to eliminate one variable to find the other

Let x^{2} + y^{2} = 6 --- (a)

x^{2} - y = 6 --- (b)

Subtract eq(b) from eq(a)

We get, y^{2 }+ y =0

⇒ y(y + 1) = 0

⇒ **y = 0, -1**

When y = 0, x^{2 }= 6

⇒** x = √6, -√6**

When y = -1, x^{2 }= 5

⇒ **x = √5, -√5**

Therefore, the solutions are (√6, 0), (-√6, 0), (√5, -1), (-√5, -1).

## Choose the solution(s) of the following system of equations: x^{2} + y^{2} = 6 and x^{2} - y = 6

**Summary:**

The solution(s) of the following system of equations: x^{2} + y^{2} = 6 and x^{2} - y = 6 are (√6, 0), (-√6, 0), (√5, -1), (-√5, -1).