1. Lesson 6-3 – Solving Systems Using Elimination
Agenda
Lesson 6-3 – Solving Systems Using Elimination
Standards
9.0 Solve a system of two linear equations in two variables algebraically.
Warm Up
Review
Notes – Elimination
Practice
Homework – Page 576 problems 7 to 12 all

2. Homework – Page 576 problems 7 to 12 all
Warm Up
Solve each system using substitution
y = 4x – 2
y = 2x + 4
b. y = 2x + 10
y = –3x
2x + 3y = 22
9x – 3y = 0
Homework – Page 576 problems 7 to 12 all

3. Substitution Method
Elimination Method – add or subtract two equations to eliminate one variable
Example – add:
3x + 2y = 14
2x – 2y = 11
to get: 5x = 25 and eliminate y to get x = 5

4. 1 EXAMPLE Adding Equations Solve by using elimination: 5x – 6y = –32
Page 287
5x – 6y = –32
3x + 6y = 48
Solve by using elimination:
Step 1: Eliminate y because the sum of the coefficients of y is 0
5x – 6y = –32
3x + 6y = 48
Step 2: Solve for the other variable in either equation
3x + 2y = 48
Check: Does 5(2) – 6(7) = –32? Yes so (2, 7) is the solution

5. Multiplying one equation
EXAMPLE 3
Multiplying one equation
Page 288
2x + 5y = –22
10x + 3y = 22
Solve by using elimination:
Step 1: Eliminate one variable
2x + 5y = –22
10x + 3y = 22
5(2x + 5y = –22)
10x + 3y = 22
10x + 25y = –110
10x + 3y =
Step 2: solve for the remaining variable
22y = –132
Step 3: solve for the eliminated variable
2x + 5(–6) = –22
Solution is (4, –6)

6. Homework – Please do at home tonight
Class work – Please do these now
Page 290/291 problems 1 to 6 and 9 to 11 all
Homework – Please do at home tonight
Page 576 problems 7 to 12 all

7. Lesson 6-3 – Solving Systems Using Elimination
Agenda
Lesson 6-3 – Solving Systems Using Elimination
Standards
9.0 Solve a system of two linear equations in two variables algebraically.
Warm Up
Review
Notes – Elimination
Practice
Homework – Finish Worksheet 6–3

8. Homework – Finish Worksheet 6–3
Warm Up
Solve each system using elimination
y = 4x – 2
y = 3x + 4
b. y = 2x + 10
y = 3x
2x + 4y = 22
8x – 4y = 8
Homework – Finish Worksheet 6–3

9. Multiplying both equations
EXAMPLE 5
Multiplying both equations
Page 290
4x + 2y = 14
7x – 3y = –8
Solve by using substitution:
Step 1: Eliminate one variable
4x + 2y = 14
7x – 3y = –8
3(4x + 2y = 14)
2(7x – 3y = –8)
12x + 6y = 42
14x – 6y = –16
Step 2: solve for the remaining variable
26x = 26
Step 3: solve for the eliminated variable
4(1) + 2y = 14
Solution is (1, 5)

10. Multiplying both equations
EXAMPLE 5a
Multiplying both equations
3x + 5y = 19
2x – 4y = –2
Solve by using substitution:
Step 1: Eliminate one variable
3x + 5y = 19
2x – 4y = –2
2(2x + 5y = 19)
3(3x – 4y = –2)
6x + 10y = 38
6x – 12y = –6
Step 2: solve for the remaining variable
22y = 44
Step 3: solve for the eliminated variable
3x + 5(2) = 19
Solution is (3, 2)

11. Homework – Please do at home tonight
Class work – Please do these now
Page 291 problems 17 to 22 all and 24 to 28 even
Homework – Please do at home tonight
Finish Worksheet 6–3