### Home > CCG > Chapter 3 > Lesson 3.2.4 > Problem3-89

3-89.

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 slope-intercept form $(y=mx+b)$. 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.

$y=2x+1$ and $y=2x-3$

Since the two lines have the same slope but different $y$-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 $2x+1=2x-3$ algebraically.

Since $1\ne-3$, there is no solution to this system of equations.