The graph of a system of two linear equations has no solution. What is true about the lines?

The lines are perpendicular.
The lines have the same slope, but different intercepts.
The lines have the same intercept, but different slopes.
The lines are on top of each other.

Solution:

Option (ii) is true.

Example:

Consider two lines whose equations are 2x +3y =8 and 2x +3y =16 which represent two parallel lines. Hence their slopes are equal. Also from the graph, we observe that their x-intercept and y-intercept are different. Since the lines do not intersect they do not have any solutions.

The graph of a system of two linear equations has no solution. What is true about the lines?

Summary:

If the graph of a system of two linear equations has no solution then lines have the same slope, but different intercepts is true