Take the value of $x$ from the first equation and plug it into $y = 2x^2 + 5$. Be careful when squaring a negative number.

Once you know both $x$ and $y$, multiply them to get $xy$. Pay special attention to the sign (positive or negative) of the product.

In Desmos, enter the parabola as y = 2x^2 + 5 on one line and the vertical line as x = -3 on another line. You will see where the line intersects the parabola.

Tap or click on the point where the vertical line $x=-3$ intersects the parabola. Desmos will display the coordinates $(x,y)$ of this intersection; these are the solution values of $x$ and $y$ for the system.

Using the $x$- and $y$-values from the intersection, type their product on a new line, for example (x-coordinate)*(y-coordinate). The resulting output is the value of $xy$ requested in the problem.

From the first equation, every solution of the system must have $x=-3$. This is the $x$-coordinate in the ordered pair $(x,y)$.

Plug $x=-3$ into $y=2x^2+5$:

Now evaluate the square first:

• $(-3)^2 = 9$ (a negative number squared becomes positive)

So

Thus, in the solution, $y=23$.

Now use the values you found: $x=-3$ and $y=23$.

Compute the product:

So the value of $xy$ is $-69$, which corresponds to choice B.