After setting $x^2 + 2x + 3$ equal to $4x + 2$, move all terms to one side so you have an equation equal to 0. Can you factor the resulting quadratic?

Once you find the value of $x$ that satisfies the quadratic, plug it into either original equation (the line or the parabola) to compute the corresponding y-value.

Use the x and y you found to form an ordered pair $(x, y)$ and then see which choice matches that exact pair.

In Desmos, type y = x^2 + 2x + 3 on one line and y = 4x + 2 on another line so both graphs (a parabola and a line) appear.

Look for the point where the line and the parabola cross. Tap or click on the intersection point; Desmos will display its coordinates $(x, y)$. These coordinates are the solution to the system.

Match the x- and y-coordinates of that intersection point with the listed answer options to see which ordered pair is correct.

At the solution, both equations have the same x and the same y, so the right-hand sides must be equal.

Now move all terms to one side to get a standard quadratic equation.

Subtract $4x+2$ from both sides:

Factor the quadratic:

So there is only one solution for $x$.

From $(x - 1)^2 = 0$, we get:

Now use this x-value in either original equation to find the matching y-value.

Substitute $x = 1$ into the linear equation $y = 4x + 2$:

So the solution to the system is the ordered pair $(1, 6)$, which corresponds to answer choice C.