Problem: For how many values of the coefficient do the equations
and
have a common real solution?
Answer Choices:
A.
B.
C.
D.
E. infinitely many
Solution:
Subtracting the second given equation from the first yields
or, equivalently,
Hence, or . If , then the given equations are identical and have (two complex but) no real solutions; is a common solution to the given equations if and only if . Therefore, two is the only value of for which the given equations have a common real solution.