1. 6-3 & 6-4 Solving Systems by Elimination
Goal: Solve systems of linear equations using elimination.
Eligible Content:
A / A

2. Vocabulary
Elimination Method – the process of adding two equations together to get a variable to cancel out.
Also called the Linear Combinations Method.
Opposites – two numbers that are the same distance from 0.

3. Steps
Multiply one or both equations by any numbers that will give you opposite coefficients for a variable.
Add the two equations together and solve for the remaining variable.
Plug your answer from Step 2 into any equation to solve for the other variable.
Write your answer as an ordered pair.
Check your answer.

4. 2x + 5y = 5 3x + 2y = -9
3 ( )
-2( )
2x + 5y = 5 3x + 2y = -9 2x + 5 * 3 = 5 2x + 15 = x = x = -5
6x + 15y = 15 -6x – 4y = 18 11y = y = 3 (-5, 3)

5. Let’s work on multiplying step only!!
What would you multiply by for each problem?
2x + 3y = 9 and 4x + 4y = 10
–5x – 2y = 10 and 3x + 7y = 12
2x + y = 5 and 3x – 4y = 14
18x + 12y = 90 and 12x + 8y = 72

6. Examples 2x + 3y = 0 4x + 3y = 16 5x – 6y = 27 2x – 3y = 8 (3, -2)
(6, 5)
4x + 3y = 16
2x – 3y = 8
(4, 0)
–2x + 3y = 12
2x – 8y = –52
(6, 8)
3x + 5y = 6
–4x + 2y = 5
(-0.5, 1.5)

7. Use elimination to solve the system of equations
Use elimination to solve the system of equations. 3x – 5y = 1 2x + 5y = 9
A. (1, 2)
B. (2, 1)
C. (0, 0)
D. (2, 2)

8. Use elimination to solve the system of equations
Use elimination to solve the system of equations. 9x – 2y = 30 x – 2y = 14
A. (2, 2)
B. (–6, –6)
C. (–6, 2)
D. (2, –6)

9. Use elimination to solve the system of equations
Use elimination to solve the system of equations. x + 7y = 12 3x – 5y = 10
A. (1, 5)
B. (5, 1)
C. (5, 5)
D. (1, 1)

10. Use elimination to solve the system of equations
Use elimination to solve the system of equations. 3x + 2y = 10 2x + 5y = 3
A. (–4, 1)
B. (–1, 4)
C. (4, –1)
D. (–4, –1)

11. Practice x + 3y = 5 2x – 3y = 1 4x – 3y = 0 2x + 4y = –22 5x + 7y = 31
(2, 1) (-3, -4) (9, -2)

12. Homework
Page 354 #8-12 even Page 360 #8-12 even