Question

What is the maximum number of possible solutions for the system shown below?

Answer 1

Answer:

B:  4 solutions

Step-by-step explanation:

Combining the two equations results in 2x² = 52, or x² = 26.

This equation has two solutions:  x = ±√26.

As before, x² = 26.  If we substitute 26 for x² in the 1st equation, we get:

26 - 4y² = 16, or 4y² = 10, or y = ±√5/2.  Again:  two solutions.

If we take x to be +√26, y could be ±√(5/2).

Check:  is ( √26, √(5/2) ) a solution of the system?

Subbing these values into the first equation, we get:

26 - 4(5/2) = 16.  Is this true?

Then 10 = 10.  Yes.

Through three more checks, we find that this system has FOUR solutions.