Answer:
infinitely many solutions
Explanation:
Let's first eliminate y^2.
To accomplish this, divide the 2nd equation by 5, obtaining
y^2 = 5/2 - x^2. Now substitute this result for y in the first equation:
(-1/3)x^2 = -5/6 + (1/3)(5/2 - x^2), or
-x^2 -5 5 x^2
-------- = ------ + ------- - -------- and this simplifies to:
3 6 6 3
-x^2 x^2
------- = - ------- which is an identity and is thus always true.
3 3
Thus, any value of x will satisfy this equation; there are infinitely many solutions.