Question 823977
I'd use substitution.


Solve the second equation for y.


2x + y = 0


y = 0 - 2x


y = -2x


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Then plug it into the first equation


5x^2 + y^2 = 9


5x^2 + (-2x)^2 = 9 ... replace every copy of 'y' with '-2x' (since y = -2x)


5x^2 + 4x^2 = 9


9x^2 = 9


x^2 = 9/9


x^2 = 1


x = +-sqrt(1)


x = sqrt(1) or x = -sqrt(1)


x = 1 or x = -1



If x = 1, then...


y = -2x


y = -2*1


y = -2


Or...if x = -1, then ...


y = -2x


y = -2*(-1)


y = 2


So the values of y are y = -2 or y = 2


So the answer is <font color="red">choice c) 2</font>