Question

David wants to solve a system of linear equations graphically. He changed both equations into slope-intercept form and he notices that the slope is same for both lines. Which of the following statements is true, based on the information provided?

• A. The system could have no solution, one solution, or infinitely many solutions
• B. The system has no solution because two equations with the same slope never intersect
• C. The system has either no solution or infinitely many solutions, depending on the $y$-intercepts
• D. The system has infinitely many solutions because two equations with the same slope represent the same line

Answer 1

The correct option is C The system has either no solution or infinitely many solutions, depending on the $y$-intercepts

If the slopes of both lines are same then the lines are parallel. Now, both the equations can represent same line or two different lines. If the equations represent the same line, then they are coincident and have infinite number of solutions, else if the equations represent two different lines with same slope then they are parallel and hence will never intersect, and therefore won't have any solution.