### Home > INT1 > Chapter Ch7 > Lesson 7.2.1 > Problem 7-92

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* = 2*x* + 1 and *y* = 2*x* − 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 2*x* + 1 = 2*x* − 3 algebraically.

Since 1 ≠ −3, there is no solution to this system of equations.