### Home > CC3MN > Chapter 9 > Lesson 9.2.1 > Problem 9-113

Do two lines *always* intersect? Consider this as you answer the questions below.

Write a system of linear equations that does not have a solution. Write each equation in your system in

form. Graph your system on graph paper and explain why it does not have a solution.Write a system of equations using two lines that have the same slope.

andSince the two lines have the same slope but different

-intercepts,

they will never intersect each other, hence there is no solution.How can you tell algebraically that a system of linear equations has

*no solution*? Solve your system of equations from part (a) algebraically and demonstrate how you know that the system has no solution.Try solving

algebraically. Since

, there is no solution to this system of equations.