Number of Solutions from Graphs

• no solution

• one unique solution

• two solutions

• an infinite number of solutions

• no solution

• one unique solution

• two solutions

• an infinite number of solutions

• The linear equations have the same slope and y-intercept.

• The linear equations have different slopes and y-intercepts.

• The linear equations have the same slope but different y-intercepts.

• The linear equations have different slopes but the same y-intercept.

• Trang is correct because the lines have the same slope but different y-intercepts.

• Trang is correct because the lines have the same slope and the same y-intercept.

• Trang is not correct because the lines have the same slope but different y-intercepts.

• Trang is not correct because the lines have the same slope and the same y-intercept.

• Each has a slope of –3 and a y-intercept of –1, which makes the lines parallel.

• Each has a slope of –3 and a y-intercept of –1, which makes the lines equivalent.

• Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines parallel.

• Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines equivalent.

Consider the graph with four lines.

By inspection, which system would have no solution?

• line a and line b

• line a and line c

• line b and line c

• line b and line d

If the four lines are extended, which system would have only one solution?

• line a and line b

• line b and line c

• line b and line d

• line c and line d

The graph represents a system of equations.

By observation, what is the solution to this system?

• (0, –3)

• (–3, 0)

• no solution

• infinitely many solutions

Miguel used the graph to represent a system of equations.

Which statement is the best conclusion for Miguel’s system?

• Since the lines do not intersect, this system has no solution.

• Since the lines will intersect at one point, this system has one solution.

• Since the lines will intersect at two points, this system has two solutions.

• Since the lines will intersect at many points, the system has many solutions.

• 
• 
• 
•