1. Solving Special Systems
Essential Question?
How can you solve a system with no solution or infinitely many solutions?
8.EE.8b

2. Common Core Standard:
8.EE.8 ─ Analyze and solve pairs of simultaneous linear equations.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

3. Objective - To solve special systems of linear equations and to identify the number of solutions a system of linear equations may have.

4. 3 Possible Outcomes 1) 2) 3) Lines Intersect Lines Parallel
Lines Coincide
(Overlap)
One
Solution No
Solution
Infinitely Many
Solutions
Consistent &
Independent
Inconsistent
Consistent &
Dependent

6. Infinitely Many Solutions

7. Solve the system graphically, by substitution, and
by elimination.
Graphic Method

8. Solve the system graphically, by substitution, and
by elimination.
Substitution

9. Solve the system graphically, by substitution, and
by elimination.
Elimination

10. Solve the system graphically, by substitution, and
by elimination.
Graphic Method
No Solution

11. Solve the system.
Substitution
False! Not true.
No Solution

12. Solve the system.
Elimination
False!
Not true.
No Solution

13. Solve the system any way you choose.
Elimination
TRUE!
They are Identical
Infinite Solutions