Question

Please help 15 points

Answer 1

Answer:

infinitely many solutions

Step-by-step 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.