Try writing one equation that does not include $y$ by setting $x^2 - 1$ equal to the other expression for $y$.

Once you have an equation involving only $x$, solve it and then see which of the answer choices gives a value of $y$ that matches $y = 8$ when plugged into $y = x^2 - 1$.

In Desmos, enter y = x^2 - 1 on one line and y = 8 on another line. You will see a parabola and a horizontal line.

Tap or click where the line and parabola intersect. Desmos will display the coordinates of these intersection points; note the $x$-values of these points.

Compare the $x$-values from the intersection points with the answer choices and select the choice that matches one of those $x$-values.

The system is

Because both expressions equal $y$, they must be equal to each other. So set the right-hand sides equal:

Solve $x^2 - 1 = 8$:

Now ask: what values of $x$ have a square of 9? That gives two possibilities:

The question asks for one possible value of $x$ that satisfies the system. From the solutions above, the possible $x$-values are $3$ and $-3$.

Look at the answer choices: $7$, $-9$, $1$, and $3$. The only choice that matches one of the correct $x$-values is $3$, so that is the correct answer.