What is the solution of each system? Use a graph.
Graph the equations
The equations represent the same line. Any point on the line is a solution of the system, so there are infinitely many solutions. The system is consistent and dependent.
If two equations have the same slope and y-intercept, their graphs will be the same line. If two equations have the same slope but different y-intercepts, their graphs will be parallel lines.
Graph the equations
The lines are parallel, so there is no solution. The system is inconsistent.
✓ Got It?
What is the solution of each system in parts (a) and (b)? Use a graph. Describe the number of solutions.
One solution
The lines intersect at one point. The lines have different slopes. The equations are consistent and independent.
Infinitely many solutions
The lines are the same. The lines have the same slope and y-intercept. The equations are consistent and dependent.
No solution
The lines are parallel. The lines have the same slope and different y-intercepts. The equations are inconsistent.