1. Solving Linear Systems
Elimination Method

2. Using Algebra Tiles Think of 2 Parties Party #1 x + y = 2 Party #2
“balanced”
“balanced

3. Now, join the parties together.+

4. After joining the parties we have …
We can marry off the y and –y …

5. After joining the parties we have …
We can marry off the y and –y …

6. After joining the parties we have …
We can marry off the y and –y …

7. Now, we are left with …
So, we solve for x …
x = 3

8. Pick either equation 1 or equation 2.
Now, solve for y …
(this step is the same as the substitution method)
Pick either equation 1 or equation 2.
Equation #1
x + y = 2
(3) + y = 2
3 – 3 + y = 2 – 3
y = -1

9. State the Solution
So, our final solution is …
(3, -1)

10. Solving By Elimination Steps
Join the two parties. (Add the 2 equations together).
“Marry off” a pair of variables. (Eliminate one of the variables).
Solve the remaining equation.
Substitute to find the second part of the solution.
State the solution.

11. Example #2 Showing With and Without Tiles
x + y = 6  (1)
x – y = 4  (2)

12. Add Equations (1) and (2) Together
x + y = 6
+ x – y = 4
2x + 0y = 10

13. “Marry Off” & Solve for Variable
2x = 10
2x ÷ 2 = 10 ÷ 2
x = 5

14. Use x to solve for y: Substitute x = 5 into Equation 1: x + y = 6

15. Write Solution
So, our solution is …
(5, 1)