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

Solution:

In order to solve two system of equations

x² + y² = 25 --- (1)

y = 2x - 5 --- (2)

Replace y with 2x - 5 from the second equation in the first equation.

x² + (2x - 5)² = 25

x² + 4x² + 25 - 20x = 25

Simplifying by separating the like terms

⇒ 5x² - 20x = 0.

On separating the common term 5x

⇒ 5x(x - 4) = 0

⇒ 5x = 0 and x - 4 = 0

⇒ x = 0 and x = 4

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

Summary:

On solving the equations x² + y² = 25, y = 2x - 5 ,the set of values of x satisfying the equation are x = 0 and x = 4. A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.