Multiple choice

Find the values of x and y that solve the given set of equations. y = 9 - x2 y = 6 - 2x

  1. x = - 1; y = 7 and x = 2; y = 1

  2. x = - 2; y = 5 and x = - 3; y = 1

  3. x = - 1; y = 8 and x = 3; y = 0

  4. x = - 2; y = 4 and x = 3; y = 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Set 9 - x^2 = 6 - 2x. Then x^2 - 2x - 3 = 0. Factoring gives (x - 3)(x + 1) = 0. If x = 3, y = 6 - 2(3) = 0. If x = -1, y = 6 - 2(-1) = 8.

AI explanation

Set the two equations equal to each other to find the intersection points: 9 - x2 = 6 - 2x. Rearranging this gives x2 - 2x - 3 = 0. Factoring this quadratic equation results in (x - 3)(x + 1) = 0, meaning the solutions for x are 3 and -1. Substituting x = 3 into y = 6 - 2x gives y = 0, and substituting x = -1 gives y = 8. The values are x = -1, y = 8 and x = 3, y = 0.

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