Multiple choice

Which point is a solution to this linear quadratic system? $y={x}^{2}+4x+3$ and $y=2x+6$

  1. $(-3,0)$
  2. $(1,-8)$
  3. $(3,0)$
  4. $(0,-3)$
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A Correct answer
Explanation

Substitute x = -3 into both equations: y = (-3)^2 + 4(-3) + 3 = 9 - 12 + 3 = 0. y = 2(-3) + 6 = -6 + 6 = 0. Since both match, (-3, 0) is a solution.

AI explanation

Set the two equations equal to each other to find the intersection points, giving x^2 + 4x + 3 = 2x + 6. Simplifying this yields the quadratic equation x^2 + 2x - 3 = 0. Factoring the quadratic gives (x+3)(x-1) = 0, so the x-coordinates are x = -3 and x = 1. Substituting x = -3 into the linear equation y = 2x + 6 gives y = 0, making the point (-3,0) a valid solution.

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