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


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

  1. 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.


    Since the two lines have the same slope but different -intercepts,
    they will never intersect each other, hence there is no solution.

  2. 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.