## Consistent, Inconsistent, and Dependent Equations

A system of equations is a set of two or more equations. According to the graphing you did earlier, when two linear equations are graphed in the same plane, the lines may be ___________________
or they may ________________________________. A third possibility for two graphed lines is that they may coincide (lie on the same line).

### Consider the system: 2x + 5y = 4 The slope is ________. 3x - 2y = 1 The slope is ________.

Now, graph this system.
Describe the relationship of the lines. _________________________(intersecting/parallel/coincide).

How many points do the lines have in common? ________________________

Since the slopes of the lines are ____________________ (same/different) but the y-intercepts are _________________________(the same/different) and the lines are _____________________ this system of equations is called inconsistent.

### Consider the system: 4x + 2y = 8 The slope is _____, the y-intercept is ________. 2x + y = 4 The slope is _____, the y-intercept iss _______.

Do you think these lines will intersect? ___________Why or why not? _____________________
____________________________________. Graph them. These two graphs look like the same line so the graphs of the equations coincide.

How many points do the lines have in common? ______________

Since the slopes on the lines are ________________________(the same/different) but the y-

intercepts are _______________________(the same/different) and the lines __________________

this system of equations is called dependent.