### Home > GC > Chapter 3 > Lesson 3.2.4 > Problem3-79

3-79.

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

 Write a system of linear equations that does not have a solution. Write each equation in your system in slope-intercept form ($y = mx + b$). Graph your system on graph paper and explain why it does not have a solution.Hint (a):Write a system of equations using two lines that have the same slope.Example (a):   $y = 2x + 1$ and $y = 2x − 3$Explanation (a):Since the two lines have the same slope but different $y$-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.Hint (b):Try solving  $2x + 1 = 2x - 3$ algebraically.Answer (b):Since $1 ≠ -3$, there is no solution to this system of equations.