Substitute the given value of $y$ into the equation $\sqrt{x+9}=y$ so that you only have $x$ in the equation.

Once you have an equation of the form $\sqrt{x+9} = \text{(number)}$, think about what operation will eliminate the square root. After that, isolate $x$.

In Desmos, enter the two equations as y = sqrt(x + 9) and y = 4 so you can see where the graphs intersect.

Use the Desmos intersection tool (or tap/click where the curves meet) and note the $x$-coordinate of the intersection of $y=\sqrt{x+9}$ and $y=4$. That $x$-value is the solution to the system.

You are given the system:

Since $y=4$, replace $y$ in the first equation with $4$ to get a single equation in terms of $x$:

To remove the square root, square both sides of the equation. When you square, be sure to square the entire left and right sides:

This simplifies to:

Now solve the linear equation $x+9=16$:

Check that $x+9 \ge 0$ so the square root is defined: $7+9=16 \ge 0$, and $\sqrt{7+9} = \sqrt{16} = 4$, which matches $y=4$. Therefore, the value of $x$ that satisfies the system is $7$.