1. Solving Systems of Equations By Elimination

2. Table of Contents
46: Warm-Up
47: How Do I Solve a System of Equations by Elimination?

3. Warm-Up
Solve the system of equations using substitution 1. x + 2y = x + 2y = y = x + 3y = -6

4. Warm Up 1
Solve the system of equations using substitution 1. x + 2y = x + 2y = - 2
x + 2y = 6
- 2y
- 2y
__________
x = -2y + 6
x + 2y = 6
-1(-2y + 6) + 2y = -2
x + 2(1) = 6 2y
- 6
+ 2y = -2
x + 2 = 6
__________ -2 -2
4y – 6 = -2
x = 4
__________
+ 6
+ 6 __ __
4y = 4
Solution:
(4, 1)
y = 1

5. Warm-Up 2
Solve the system of equations using substitution 2. y = x + 3y = -6
-2x + 3(2) = -6
Solution:
-2x + 6 = -6
(6, 2)
__________ -6 -6
___ -2
-2x = -12
___ -2
x = 6

6. Learning Intention/Success Criteria
LI: We are learning how to solve a system of equations by elimination SC: I know how to -determine if a system of equations has many, one, or no solutions -solve systems of two linear equations algebraically using the elimination method -multiply by integers -add and subtract integers

7. EQ: How Do I Solve a System of Equations by Elimination?
11/29/2018

8. Fold the paper in half, hamburger style

9. Fold sides to the middle fold

10. Fold in half

12. Same coefficient, different signs

13. Same coefficient, different signs
Open flap

14. { __ 6 Solve by elimination 4x + 5y = 9 -4x + y = 3
2. Substitute value into eq. {
4x + 5y = y = 2
1. Add equations together
4x + 5(2) = 9
4x + 10 = 9
4x + 5y = 9 -4x + y = 3
-10
-10 + + +
4x = -1
__ 4
__ 4
6y = 12
__ 6
__ 6
x = -1/4
y = 2
3. Solution
(-1/4, 2)

15. { Guided Practice 1 2x + y = 10 x = 4 2(4) + y = 10 8 + y = 10 -8 -8 +
Find the solution to the system by elimination:
2x + y = x = 4
2x + y = 10 5x – y = 18 {
2(4) + y = 10
8 + y = 10
2x + y = 10 5x – y = 18 -8 -8 + + +
y = 2
7x = 28
__ 7
__ 7
Solution:
x = 4
(4, 2)

16. Same coefficient, different signs Same coefficient, same signs

17. Same coefficient, different signs Same coefficient, same signs
Open flap

18. { Solve by elimination 2x + 3y = 2 x + 3y = 7 + + +
3. Substitute value into equation {
2x + 3y = x = -5
1. Multiply one eq. by -1
2(-5) + 3y = 2
2x + 3y = 2 x + 3y = 7
y = 2
-1( )
+ 10
+ 10
2x + 3y = 2 -x - 3y = -7
3y = 12
__ 3
__ 3
2. Add eqs together
y = 4
2x + 3y = 2 -x - 3y = -7 + + +
(-5, 4)
4. Solution:
x = -5

19. Guided Practice 2
Find the solution to the system by elimination:
-x - 5y = x + 5y = -6 + + + {
x + 5y = 33 -2x + 5y = -6
-3x = -39
__ -3
__ -3
x = 13
-1 ( )
x + 5y = 33 -2x + 5y = -6
x + 5y = x = 13
13 + 5y = 33
-x - 5y = x + 5y = -6
-13
-13
5y = 20
__ 5
__ 5
Solution:
(13, 4)
y = 4

20. Same coefficient, different signs Same coefficient, same signs
Different coefficients, multiply one equation

21. Same coefficient, different signs Same coefficient, same signs
Different coefficients, multiply one equation
Open flap

22. { Solve by elimination 3x + y = 7 x + 2y = 34 ___ -5 ___ -5 x = -4
3. Substitute value into equation
1. Multiply eq. by # to make same coefficients
-2( )
3x + y = x = -4
3x + y = x + 2y = 34
3(-4) + y = 7
-12 + y = 7
-6x + -2y = x + 2y = 34
+12
+12
y = 19
2. Add eqs together
-6x + -2y = x + 2y = 34
4. Solution + + +
(-4, 19)
-5x = 20

23. Guided Practice 3
Find the solution to the system by elimination:
x – 2y = y = -1 {
x – 2y = 5 4x + 3y = 9
x – 2(-1) = 5
x + 2 = 5
-4( )
x – 2y = 5 4x + 3y = 9 -2 -2
x = 3
-4x + 8y = x + 3y = 9 + + +
Solution:
11y = -11
___ 11
___ 11
(3, -1)
y = -1

24. Same coefficient, different signs Same coefficient, same signs
Different coefficients, multiply one equation
Different coefficients, multiply both equations

25. Open flap Same coefficient, different signs
Same coefficient, same signs
Different coefficients, multiply one equation
Different coefficients, multiply both equations
Open flap

26. { Solve by elimination 4x – 3y = 25 -3x + 8y = 10 23y = 115 ___ 23
___ 23
___ 23
y = 5
3. Substitute value into equation
1. Multiply eqs. by # to make same coefficients
4x – 3y = y = 5
4x – 3y = x + 8y = 10
3( )
4x – 3(5) = 25
4( )
4x – 15 = 25
12x + -9y = x +32y = 40
+15
+15
4x = 40
___ 4
___ 4
2. Add eqs together
12x + -9y = x +32y = 40
x = 10 + + +
4. Solution
23y = 115
(10, 5)

27. { Guided Practice 4 Find the solution to the system by elimination:
3x – 2y = -5 x = 3 {
8x – 3y = 3 3x – 2y = -5
3(3) – 2y = -5
9 – 2y = -5
-2( )
8x – 3y = x – 2y = -5 -9 -9
3( )
– 2y = -14
___ -2
__ -2
-16x + 6y = x – 6y = -15
y = 7
-7x = -21
__ -7
__ -7
Solution:
(3, 7)
x = 3