### Home > CC4 > Chapter 7 > Lesson 7.1.7 > Problem 7-81

Do two lines always have *only one* intersection point? Consider this as you answer the questions below. Homework Help ✎

Write a system of linear equations that has an

*infinite*number of solutions. Write your equations in*y = mx + b*form and graph your system on graph paper. Explain why it has an infinite number of solutions.How can you algebraically determine that a system of linear equations has an

*infinite number of solutions*? Solve your system of equations from part (a) algebraically and demonstrate how you know that the system has an infinite number of solutions

Write a system of equations using two lines that have the same slope and the same *y*-intercept.

Since the two lines have the same slope and the same *y*-intercept, the lines coincide (overlap).

So all of the points are solutions for both equations.

Try solving 2*x* + 1 = 2*x* + 1 algebraically.

Subtracting 2*x* on both sides results in 1 = 1 which is a true statement. Therefore, there are an infinite number of solutions to this equation.