1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use the elimination method to solve a system of equations. Choose an appropriate method to solve a system of equations. 7.3 The Elimination Method

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Term elimination method 7.3 The Elimination Method

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Summary of Methods for Solving Systems 7.3 The Elimination Method Substitution The value of one variable is known and can easily be substituted into the other equation. 6x + y = 10 y = 5 Example Suggested Method Why

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Summary of Methods for Solving Systems 7.3 The Elimination Method Elimination 5y and –5y are opposites and are easily eliminated. 2x – 5y = –20 4x + 5y = 14 Example Suggested Method Why

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Summary of Methods for Solving Systems 7.3 The Elimination Method Elimination b can easily be eliminated by multiplying the first equation by –2. 9a – 2b = –11 8a + 4b = 25 Example Suggested Method Why

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Summary of Methods for Solving Systems 7.3 The Elimination Method Graphics Calculator The coefficients are large numbers, so other methods may be cumbersome. 324p + 456t = 225 178p – 245t = 150 Example Suggested Method Why

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills 7.3 The Elimination Method Find an exact solution to a system of equations by using the elimination method. Step 1:Multiply as needed. 5x + 3y = 76 3(2x) – 3y = 3(4) Solve 5x + 3y = 76 2x – y = 4

8. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills 7.3 The Elimination Method Find an exact solution to a system of equations by using the elimination method. Step 3:Combine to eliminate. 5x+3y=76 6x–3y=12 11x=88 x=8x=8 5x + 3y = 76 3(2x) – 3y = 3(4) Solve

9. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills 7.3 The Elimination Method Find an exact solution to a system of equations by using the elimination method. Step 4:5x+3y=76 x=8x=8 5(8)+3y=76 40+3y=76 3y=36 y=12 Solve 5x + 3y = 76 6x – 3y = 12

10. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills 7.3 The Elimination Method Find an exact solution to a system of equations by using the elimination method. Solution:(8, 12) x=8x=8 y = 12 Solve 2.5y = 17 – 3x 4x + 5y = 29 TOC