1. Solving Systems of Equations:
Elimination Method
Mr. Pearson Inman Middle School February 2, ACCELERATED

2. BY GRAPHING Y = 2X + 1 Y = -X + 4 (1,3) IS THE SOLUTION
(1,3) IS THE SOLUTION
GPS STANDARD: M8A5.b Solving Systems Graphically and Algebraically.

3. Graphing is not the only way to solve a system of equations
Graphing is not the only way to solve a system of equations. We already know a second method called SUBSTITUTION. We have yet another way to solve. This method is called the ELIMINATION Method. You solve by eliminating one variable.

4. Solve: by ELIMINATION x + y = 12 -x + 3y = -8
Like variables must be lined under each other.
Solve: by ELIMINATION x + y = 12 -x + 3y = -8
4y = 4
We need to eliminate (get rid of) a variable.
The x’s will be the easiest. So, we will add the two equations.
Divide by 4
y = 1
THEN----

5. Now check our answers in both equations------
Substitute your answer into either original equation and solve for the second variable.
X +Y = 12
x + 1 = 12
x = 11
(11,1)
Answer
Now check our answers in both equations------

6. X + Y =12
= 12
12 = 12
-x + 3y = -8
(1) = -8
= -8
-8 = -8

7. Solve: by ELIMINATION 5x - 4y = -21 -2x + 4y = 18
Like variables must be lined under each other.
Solve: by ELIMINATION 5x - 4y = x + 4y = 18
3x = -3
We need to eliminate (get rid of) a variable.
The y’s be will the easiest.So, we will add the two equations.
Divide by 3
x = -1
THEN----

8. Now check our answers in both equations------
Substitute your answer into either original equation and solve for the second variable.
5X - 4Y = -21
5(-1) – 4y = -21
-5 – 4y = -21
-4y = -16
y = 4
(-1, 4)
Answer
Now check our answers in both equations------

9. 5x - 4y = -21 5(-1) – 4(4) = -21 -5 - 16 = -21 -21 = -21
-2(-1) + 4(4) = 18
= 18
18 = 18

10. Solve: by ELIMINATION 2x + 7y = 31 5x - 7y = - 45
Like variables must be lined under each other.
Solve: by ELIMINATION 2x + 7y = 31 5x - 7y = - 45
We need to eliminate (get rid of) a variable.
The y’s will be the easiest. So, we will add the two equations.
Divide by 7
7x =
x = -2
THEN----

11. Now check our answers in both equations------
Substitute your answer into either original equation and solve for the second variable.
2X + 7Y = 31
2(-2) + 7y = 31
-4 + 7y = 31
7y = 35
y = 5
(-2, 5)
Answer
Now check our answers in both equations------

12. 2x + 7y = 31 2(-2) + 7(5) = = = 31
5x – 7y = - 45
5(-2) - 7(5) = - 45
= - 45
- 45 =- 45

13. Solve: by ELIMINATION x + y = 30 x + 7y = 6
Like variables must be lined under each other.
Solve: by ELIMINATION x + y = 30 x + 7y = 6
We need to eliminate (get rid of) a variable.
To simply add this time will not eliminate a variable. If one of the x’s was negative, it would be eliminated when we add. So we will multiply one equation by a – 1.

14. X + Y = 30 X + Y = 30 -X – 7Y = - 6 ( X + 7Y = 6 ) -1 -6Y = 24 - 6 - 6
Now add the two equations and solve.
- 6
- 6
Y = - 4
THEN----

15. Now check our answers in both equations------
Substitute your answer into either original equation and solve for the second variable.
X + Y = 30
X = 30
X = 34
(34, - 4)
Answer
Now check our answers in both equations------

16. x + y = = = 30
x + 7y = 6
34 + 7(- 4) = 6
= 6
6 = 6

17. Solve: by ELIMINATION x + y = 4 2x + 3y = 9
Like variables must be lined under each other.
Solve: by ELIMINATION x + y = 4 2x + 3y = 9
We need to eliminate (get rid of) a variable.
To simply add this time will not eliminate a variable. If there was a –2x in the 1st equation, the x’s would be eliminated when we add. So we will multiply the 1st equation by a – 2.

18. ( ) -2 Y = 1 THEN---- X + Y = 4 -2X - 2 Y = - 8 2X + 3Y = 9
Now add the two equations and solve.
THEN----

19. Now check our answers in both equations------
Substitute your answer into either original equation and solve for the second variable.
X + Y = 4
X + 1 = 4
X = 3
(3,1)
Answer
Now check our answers in both equations------

20. x + y = = = 4
2x + 3y = 9
2(3) + 3(1) = 9
6 + 3 = 9
9 = 9