Solve the following system of equations algebraically:y, equals, x, squared, plus, 6, x, minus, 6y=x 2 +6x−6y, equals, 3, x, minus, 2y=3x−2

Question

Solve the following system of equations algebraically:y, equals, x, squared, plus, 6, x, minus, 6y=x 2 +6x−6y, equals, 3, x, minus, 2y=3x−2
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Solution 1

The system of equations is:

  1. y = x^2 + 6x - 6
  2. y = 3x - 2

To solve this system algebraically, we can set the two equations equal to each other because they both equal y:

x^2 + 6x - 6 = 3x - 2

Next, we can simplify this equation by subtracting 3x and adding 2 to both sides:

x^2 + 3x - 4 = 0

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