solving 2nd dregree equation

Question

Solve the system:

4x^2+9y^2=36

x^2-4y^2=16

Answer 1

No real solution.

Notice that since x^2 - 4y^2 = 16, we have 4x^2 - 16y^2 = 64

16y^2 >= 0, since the square of a real number is non-negative.

This means that 4x^2 + 9y^2 >= 4x^2 - 16y^2

However, 36 < 64 instead.

Hence, there is no real solution.