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# What are the x-coordinates of the solutions to this system of equations?

x^{2} + y^{2} = 100, y = x + 2

**Solutions:**

x^{2} + y^{2} = 100 , y = x + 2

**Given system of equations:**

x^{2} + y^{2} = 100 --- (1)

y = x + 2 --- (2)

**Replace y = x + 2 in equation 0 gives**

x^{2} + (x + 2)^{2} = 100

(a + b)^{2} = a^{2} + 2ab + b^{2}

**Changes above equation to**

x^{2} + x^{2} + 4x + 4 = 100

2x^{2} + 4x = 100 - 4

2x^{2} + 4x = 96

**Dividing by 2 on both sides so that the equation reduces to simplified from**

x^{2} + 2x = 48

x^{2} + 2x - 48 = 0

**On solving by factorization method**

x^{2} + 8x - 6x - 48 = 0

x(x + 8) - 6(x + 8) = 0

## What are the x-coordinates of the solutions to this system of equations?

x^{2} + y^{2} = 100, y = x + 2

**Summary:**

The x-coordinates of the solutions to this system of equations x^{2} + y^{2} = 100 , y = x + 2 are 6, -8.

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