If x² + y = 13 and x² - y = 5, what is the product of the two possible values of x?

Add the equations to eliminate $y$: $2x^2 = 18$, so $x^2 = 9$ and $x = 3$ or $x = -3$. The two possible values of $x$ have the product $3 \times (-3) = -9$, choice D. Check: $y = 13 - 9 = 4$ and $9 - 4 = 5$. Choice A (9) is $x^2$ and drops the sign of the product. Choice B (4) is the value of $y$. Choice C (3) is one of the values of $x$ rather than the product of both. The product of a number and its opposite is always negative: $-x^2$.