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