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 y = mx + b form. Graph your system on graph paper and explain why it does not have a 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.
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.
Try solving 2x + 1 = 2x − 3 algebraically.
Since 1 ≠ −3, there is no solution to this system of equations.