Replace $y$ with $x - 1$ in $x^2 + y^2 = 25$. After substituting, carefully expand $(x - 1)^2$ and combine like terms.

Once you have a quadratic equation in $x$, try to factor it. What two numbers multiply to give the constant term and add to give the coefficient of $-x$?

Use $y = x - 1$ to find $y$ for each $x$ you found. Then check which of the resulting ordered pairs appears in the answer choices and still satisfies $x^2 + y^2 = 25$.

In Desmos, enter the equation x^2 + y^2 = 25. This will graph the circle of radius 5 centered at the origin.

On a new line in Desmos, enter y = x - 1. This will graph the straight line that might intersect the circle at up to two points.

Click or tap on each point where the line and circle intersect; Desmos will display the coordinates of these intersection points. Compare those coordinates to the answer choices and select the option whose ordered pair matches one of the intersection points.

From the second equation, we know $y = x - 1$.

Substitute $y = x - 1$ into the first equation $x^2 + y^2 = 25$ so that the equation has only $x$ in it.

After substitution, the first equation becomes

Now expand and combine like terms:

So

Divide both sides by $2$ to simplify:

Factor the quadratic equation:

So the possible $x$-values are

Use $y = x - 1$ to find $y$ for each $x$:

• If $x = 4$, then $y = 4 - 1 = 3$, giving the point $(4,3)$.
• If $x = -3$, then $y = -3 - 1 = -4$, giving the point $(-3,-4)$.

Both points satisfy the original circle equation, but only one of them appears in the answer choices. The ordered pair that satisfies both equations and is listed among the options is $(4,3)$.