1. 7.4 Consistent and Inconsistent Systems
Objectives: Identify consistent and inconsistent systems of equations. Identify dependent and independent systems of equations.
Standards addressed: H: Graph a linear function F: Identify whether systems of equations are consistent or inconsistent.

2. A system of equations may have one unique solution, infinitely many solutions, or no solution at all.
Systems that have one or infinitely many solutions are called consistent.
Systems with no solutions are called inconsistent.

5. Ex. 1

8. Ex. 2b. Determine whether the system is consistent or inconsistent by solving it algebraically and graphically.
Multiply 1st EQ by -2
-2x – 6y = -2
2x + 6y = 3
0 = 5
Inconsistent
No solution

9. Ex. 3a.

10. Ex. 3b Multiply 2nd EQ by -2 4y = -2x – 6 -4y = 2x + 6 0 = 0 Dependent
infinity

11. Ex. 4