16Hit1600
Advanced MathVery hardChoosing k so a system has no solution

Advanced Math practice question

For which value of k does the system y = x² + 3 and y = k have NO solution?

  1. A. k = 2Correct
  2. B. k = 3
  3. C. k = 4
  4. D. k = 7

Answer: A. k = 2

x² + 3 is always at least 3, so y = k meets the parabola only when k ≥ 3. k = 2 gives no solution.

Why the other answers are wrong

B. k = 3
k = 3 touches the vertex: one solution.
C. k = 4
k = 4 gives x² = 1: two solutions.
D. k = 7
k = 7 gives x² = 4: two solutions.

More Advanced Math questions

Not affiliated with the College Board. SAT is a trademark of the College Board.