Question

Consider the following system of equations:
-1/3xsquared =5/6+ 1/3y squared
5ysquared = 25/2 - 5xsquared
How many solutions does the system have?

zero

one

two

three

four

infinitely many

Answer 1

Interpret x^2 = X ≥ 0 and y^2 = Y ≥ 0. From the first equation:

-(1/3)X = 5/6 + (1/3)Y
Multiply by 3: -X = 5/2 + Y → X + Y = -5/2.

But X + Y ≥ 0 for real x,y, so X + Y = -5/2 is impossible. Therefore there are no real solutions.

Answer: zero.