What are the x-coordinates of the solutions to this system of equations?
x² + y² = 100, y = x + 2

Solutions:

x² + y² = 100 , y = x + 2

Given system of equations:

x² + y² = 100 --- (1)

y = x + 2 --- (2)

Replace y = x + 2 in equation 0 gives

x² + (x + 2)² = 100

(a + b)² = a² + 2ab + b²

Changes above equation to

x² + x² + 4x + 4 = 100

2x² + 4x = 100 - 4

2x² + 4x = 96

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

x² + 2x = 48

x² + 2x - 48 = 0

On solving by factorization method

x² + 8x - 6x - 48 = 0

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

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What are the x-coordinates of the solutions to this system of equations?
x² + y² = 100, y = x + 2

Summary:

The x-coordinates of the solutions to this system of equations x² + y² = 100 , y = x + 2 are 6, -8.