### Home > A2C > Chapter 8 > Lesson 8.1.2 > Problem8-28

8-28.

Consider the system of equations at right.

1. Solve the system graphically.

The first equation is a circle with radius $5$ and center $\left(0, 0\right)$.

The second equation is a parabola with vertex $\left(0, 3\right)$.

2. Now solve the system algebraically. In this case, which variable is easier to solve for first? Do it. Now try to solve for the other variable first. What caused you to get stuck?

What happens when you substitute for y in the first equation?

Try solving for $x^{2}$ in the second equation and substituting that into the first equation.

$x^{2} + y^{2} = 25\\ y = x^{2} + 3$