1. Another method for solving systems of linear equations
Elimination
Another method for solving systems of linear equations

2. We have 3 methods to solve systems:
1. By graphing
2. By substitution
3. By elimination
Today we are going to learn the final method.

3. Goal of this method: Eliminate
Elimination comes from the word ___________
The goal of this method is going to be to eliminate one of the variables in order to solve for the other variable.

4. Example 1:
Solve:
First, let’s look at which two variables are opposites of each other.
2x and -2x are opposites of each other.
So let’s eliminate the x by adding these two equations together.

5. Example 1: (cont.) +

6. Example 1: (cont.)
We have half of our point ( , 4), so now let’s plug in 4 for y and find x.

7. Example 1: (cont.)
Since we can now plug this into one of our two equations to find out what x is.

8. Example 1: (answer)
We now know the coordinates of our solution to this system. The answer is (2, 4).

9. Practice:
1. Solve:
2. Solve:

10. A possible twist:
Sometimes the variables might not already be opposites. Instead they might be the same. In this case, we would subtract the two equations to eliminate one of the variables.

11. Example 2:
Solve:
First, let’s look at which two variables are the same.
2x and 2x are the same.
So let’s eliminate the x by subtracting the second equation from the first.

12. Example 2: (cont.) -
We have half of our point ( , -2), so now let’s plug in -2 for y and find x.

13. Example 2: (cont.)
Since we can now plug this into one of our two equations to find out what x is.

14. Example 2: (answer)
We now know the coordinates of our solution to this system. The answer is (-3, -2).

15. Practice:
3. Solve:
4. Solve: