What are the x coordinates of the solutions to this system of equations x² + y² = 25 and y = 2x + 5?

To find the x coordinates of the solutions to the system of equations, we start by substituting the second equation into the first. The first equation is a circle with radius 5, centered at the origin, while the second equation represents a straight line.

The equations are:

• x² + y² = 25
• y = 2x + 5

We can substitute y in the first equation:

x² + (2x + 5)² = 25

Expanding the second term:

x² + (4x² + 20x + 25) = 25

Simplifying:

5x² + 20x + 25 = 25

Now we subtract 25 from both sides:

5x² + 20x = 0

Factoring out the common term:

5x(x + 4) = 0

This gives us the solutions:

• x = 0
• x = -4

Thus, the x coordinates of the solutions to the system of equations are 0 and -4.