1. Warm-up
Solve the first system of equations by the Substitution Method, then graphing

3. Solving Linear Systems Algebraically with Elimination
Section 3-2
Pages

4. Objectives I can use the elimination method to solve equations
I can set up and solve word problems using elimination

5. Elimination Method GOAL
1. Add the equations together and have one variable term go away.
2. Sometimes you will have to multiply one or both equations by a number to make this happen.

6. Example 1
Now, PLUG this back into
Either equation to find “y”

7. It is ALWAYS an Ordered Pair
What does this mean?
Remember that a solution to a system of equations is where the graphs cross
It is ALWAYS an Ordered Pair

8. Multiplying by a number?
Many times you cannot add the equations and have a variable term cancel
For these cases, you must multiply One or Both equations by a number first
Let’s look at a few

9. What to Multiply by?
x-variable will cancel
y-variable will cancel

10. Example 2

11. Your Turn
Solve the following system of equations using elimination:

12. Other Methods
Remember, the solution to a system of equations if an ordered pair
You know 2 other methods to check your answers:
Graphing Calculator and asking for the intersection (2nd, Trace, Intersection, E, E, E)
Substitution Method

13. Solution Types
Remember there are 3 types of solutions possible from a system of equations!

14. No Solution vs Infinite
How will you know if you have No Solution or Infinite Solutions when solving by Substitution??

15. Remember Back to Solving Equations
No Solution
Infinite Solutions
Variables are gone and you get this:
2x + 3 = 2x – 4
3 = -4
This is not possible, so
No Solution
Variables are gone and you get this:
2x + 3 = 2x + 3
3 = 3
This is always true, so
Infinite Solutions

16. Word Problems When solving a word problem, consider these suggestions
1. Identify what the two variables are in the problem
2. Write equations that would represent the word problem, looking for key words
Sum, difference, twice, product, half, etc…

17. Example 1
GEOMETRY: The length of a rectangle is 8 cm more than twice the width. If the perimeter is 40 cm, find the dimensions.
Variables:
Length (L)
Width (W)
Equations:
L = 2W + 8
2L + 2W = P
Now, solve by elimination

18. Example 2
Rental car agency A charges $8 per day plus $.20 per mile. Rental car company B charges $10, but only $.10 per mile. At what mileage is it better to use Company B?
Cost (C)
Miles (M)
Equations:
C = M
C = M
Now, solve by Elimination

19. Homework
Elimination Worksheet