1. Systems of Equations and Inequalities in Two Variables
A-REI.3; A-REI.5; A-REI.6; A-REI.7

2. Table of Contents
28: Guided Practice
29: How Do I Solve Systems of Equations with Elimination?

3. EQ: How Do I Solve Systems of Equations with Elimination?
4/19/2017

4. System of Equations
A collection of 2 or more lines, including nonlinear equations
Elimination Method
One variable is eliminated by adding or subtracting the two equations of the system to obtain a single equation in one variable

5. 1. Add or subtract the equations to eliminate one variable.
2. Solve the resulting equation for the other variable
3. Substitute the value into the original equation to find the value of the eliminated variable.

6. One Solution
The two lines cross each other in exactly one point on the graph
x = a
The two lines on the graph lie on top of each other.
Infinite Solutions
a = a
The two lines never cross.
No Solution
a = b

7. Example 1: Use elimination to solve the system of equations
2x – 3y = 12 + + +
____________
x + 3y = 6
3x = 18
__ 3
__ 3
x = 6
x + 3y = 6
6+ 3y = 6
2x – 3y = 12
x + 3y = 6
__________ -6 -6
3y = 0
__ 3
__ 3
y = 0
Solution:
(6, 0)

8. Guided Practice 1
Using the elimination method, solve the system of equations
2x + 2y = -2 3x – 2y = 12

9. Guided Practice 2
Using the elimination method, solve the system of equations
6x + 5y = 4 -6x + 7y = 20

10. Guided Practice 3
Using the elimination method, solve the system of equations
x + y = -1 x – y = 7

11. Questions
You’ve already found the x-value. Does it matter which equation you use to find the y-value? Why?
How could you check your answer?
How do you know which variable to eliminate first?

12. Example 2: Use elimination to solve the system of equations
3x + 3y = 6 – – –
3x – y = -6
____________
4y = 12
__ 4
__ 4
y = 3
3x – y = 6
3x – 3 = -6
3x + 3y = 6
3x – y = -6
__________ +3 +3
3x = -3
__ 3
__ 3
x = -1
Solution:
(-1, 3)

13. Guided Practice 4
Using the elimination method, solve the system of equations
6x – 3y = 6 6x + 8y = -16

14. Guided Practice 5
Using the elimination method, solve the system of equations
4x + 3y = 19 6x + 3y = 33

15. Guided Practice 6
Using the elimination method, solve the system of equations
2x + 6y = 17 2x – 10y = 9

16. Questions
How can you decide whether to add or subtract to eliminate a variable in a system of equations?
What do you think would happen if you couldn’t add or subtract while using the elimination method? Do you think there would be a way to solve the problem?

17. Example 3: Use elimination to solve the system of equations
2x + 10y = 2 3x – 5y = -17
2( )
______________
2x + 10y = 2 6x – 10y = -34 + + +
______________
8x = -32
__ 8
__ 8
x = -4
2x + 10y = 2
2x + 10y = 2 3x – 5y = -17
2(-4) + 10y = 2
y = 2
______________ +8 +8
__ 10
__ 10
10y = 10
(-4, 1)
y = 1

18. Guided Practice 7
Using the elimination method, solve the system of equations
x – 3y = 4 -5x + 15y = -20

19. Guided Practice 8
Using the elimination method, solve the system of equations
9x + y = 9 3x – 2y = -11

20. Guided Practice 9
Using the elimination method, solve the system of equations
x – 3y = 4 -5x + 15y = -20

21. Questions
Do you think you could multiply the top and bottom by different numbers to solve systems with elimination? Why or why not?
When you solve a system by elimination, how can you tell if there is zero, one, or infinite solutions?

22. Classwork/Homework
For classwork/homework, please do the worksheet provided. It will be due on Monday.
Solving solutions and answers are on the class website 