After substitution, you should get an equation involving only $x$. Simplify it into standard quadratic form $ax^2 + bx + c = 0$ and solve for $x$ by factoring.

Each $x$ value gives a corresponding $y$ using $y = x + 1$. You will have two $(x, y)$ pairs; compute $xy$ for both and notice what they have in common.

In Desmos, enter the equation y = x + 1 to graph the line.

In a new line, enter x^2 + y^2 = 25 to graph the circle of radius 5 centered at the origin.

Click on each point where the line and the circle intersect. Desmos will display the coordinates of each intersection as $(x_1, y_1)$ and $(x_2, y_2)$ (with specific numbers).

Pick one intersection point and note its coordinates, say $(a, b)$. In a new expression line, type a * b using those specific numbers. The output is the value of $xy$; if you repeat with the other intersection point, you will see the product is the same.

Use the first equation $y = x + 1$ and substitute into the second equation $x^2 + y^2 = 25$.

Now expand $(x+1)^2$.

Expand and combine like terms:

Subtract 25 from both sides:

Divide the entire equation by 2:

Factor the quadratic:

So $x = -4$ or $x = 3$.

Use $y = x + 1$ to find each $y$:

• If $x = -4$, then $y = -4 + 1 = -3$.
• If $x = 3$, then $y = 3 + 1 = 4$.

The two intersection points are $(-4, -3)$ and $(3, 4)$.

Now find $xy$ for each point:

• For $(-4, -3)$, $xy = (-4)(-3)$.
• For $(3, 4)$, $xy = (3)(4)$.

Both products are equal to $12$, so the value of $xy$ is $\boxed{12}$.