Question

What is a solution to the system? y = x^2 + 2x - 15 y – 4x = -12

Answer 1

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Answer:

  (x, y) = (-1, -16) or (3, 0)

Step-by-step explanation:

Perhaps you want to solve the system of equations ...

• y = x^2 +2x -15
• y -4x = -12

Substituting the first expression for y into the second equation gives ...

  x^2 +2x -15 -4x = -12

  x^2 -2x -3 = 0 . . . . . . . . add 12

  (x -3)(x +1) = 0 . . . . . . .  factor

Solutions are the values of x that make the factors zero: x = 3, x = -1.

The corresponding values of y are ...

  y = -12 +4x

  y = -12 +4{-1, 3} = -12 +{-4, 12} = {-16, 0}

The solutions to the system are ...

  (x, y) = (-1, -16) or (3, 0)