Intersecting Lines

For which real values of m are the simultaneous equations
y = mx + 3
y = (2m – 1)x + 4
satisfied by at least one pair of real numbers (x, y)?
  1. all m > 0
  2. all m ≠ 0
  3. all m ≠ .5
  4. all m ≠ 1
  5. all values of m


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The simultaneous equations will have a real solution unless the lines are parallel. The lines are parallel if their slopes are the same, that is, when m = 2m – 1, or m = 1. The answer is (d).

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