1. The document discusses solving systems of equations using substitution and elimination methods. 2. It provides examples of using substitution by solving one equation for a variable and substituting it into the second equation. 3. It also gives examples of using elimination by multiplying equations appropriately and adding or subtracting them to eliminate one variable.

1. 3.2 + 3.3 kids notes Substitution.notebook September 11, 2012
Objective ­ solve systems using substitution and elimination
Agenda
1. WU
2. Check HW Warm Up
3. Notes
4. HW
Simplify
­(4x ­ 5) + 2(x + 6)
SUBSTITUTION This method works well when a variable is already by itself.
1. x = 2y + 5
4x + 3y = 9
Steps:
1. Solve
2. Substitute
3. Solve
4. Substitute
1

2. 3.2 + 3.3 kids notes Substitution.notebook September 11, 2012
2. y = 2x
4x ­ y = 6
3. 3x + 2y = 7
x ­ 2y = ­3
2

3. 3.2 + 3.3 kids notes Substitution.notebook September 11, 2012
4.
Equations: 3x ­ y = 5
4x + 2y = 10
Sage 1: Solve one equation for a variable:
S2_____
Sage 2: Substitute answer into the second equation and solve.
S1_____
Sage 1: Substitute answer and solve for the second variable.
S2_____
Sage 2: State the solution.
S1_____
5.
Equations: 2x + y = 3
3x + y = 0
Sage 1: Solve one equation for a variable:
S2_____
Sage 2: Substitute answer into the second equation and solve.
S1_____
Sage 1: Substitute answer and solve for the second variable.
S2_____
Sage 2: State the solution.
S1_____
3

4. 3.2 + 3.3 kids notes Substitution.notebook September 11, 2012
Section 3.2 p 135
# 11 ­ 16 all
discuss
Linear Combination Goal ­ eliminate one variable
Look for opposites.
6. 3x ­ 2y = 4
4x + 2y = 10
4

5. 3.2 + 3.3 kids notes Substitution.notebook September 11, 2012
7. 4x + 3y = 5
2x ­ 5y = ­17
4x + 3y = 5
2x ­ 5y = ­17
Steps:
1. Multiply
2. Add
2. Substitute
8. ­3x + 5y = ­6
6x ­ 10 y = 12
5

6. 3.2 + 3.3 kids notes Substitution.notebook September 11, 2012
9. 2x ­ 3y = 6
4x ­ 5y = 8
6