System of Equations Help?

Question

Find all solutions algebraically to the following system of equations.

y = x^2 - 4x - 2

y = x - 2

Answer 1

y = x² - 4x - 2

y = x - 2

x² - 4x - 2 = x - 2

x² - 4x - x -2 + 2 = 0

x² - 5x = 0

x(x - 5) = 0

x = 0, or x = 5

From y = x - 2 above:

y = 0 - 2

y = -2

y = 5 - 2

y = 3

Solution set: (0, -2)(5,3)

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y = x² + 1

y - x = 1, or y = x + 1

x² + 1 = x + 1

x² - x + 1 - 1 = 0

x² - x = 0

x(x - 1) = 0

x = 0, or x = 1

From y = x + 1 above:

y = x + 1

y = 0 + 1

y = 1

y = 1 + 1

y = 2

Solution set: (0, 1)(1, 2)

Answer 2

x² - 4x - 2 = x - 2

x² - 5x = 0

x(x-5) = 0

x = 0 or 5

y = x - 2

y = -2 or 3.

2) x + 1 = x² + 1

x² - x = 0

x(x-1) = 0

x = 0 or 1

y = x+1

y = 1 or 2.