1. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 2 4.1 Systems of Linear Equations in Two Variables Systems of Equations Suppose we wished to cut a 10-foot length of conduit into two pieces such that one piece is 4 feet longer than the other. We are looking for two numbers whose sum is 10 and whose difference is 4. If we let x represent the larger of the two numbers and y the other number, we immediately get two equations. We call such an arrangement a system of two equations in two variables.

3. Sec 5.1 - 3 4.1 Systems of Linear Equations in Two Variables Solution of a Systems of Equations Given the following system of equations, determine whether the given ordered pair is a solution of the system. The ordered pair must be a solution of both equations to be a solution.

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 4 4.1 Systems of Linear Equations in Two Variables Deciding Whether an ordered Pair is a Solution Given the following system of equations, determine whether the given ordered pair is a solution of the system.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 5 4.1 Systems of Linear Equations in Two Variables Possible Solutions for a Linear System of Two Variables

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 6 4.1 Systems of Linear Equations in Two Variables The Substitution Method for Solving Systems

7. 4.1 Systems of Linear Equations in Two Variables Solving a System by Substitution

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 8 4.1 Systems of Linear Equations in Two Variables The Elimination Method for Solving Systems

9. 4.1 Systems of Linear Equations in Two Variables Solving a System by Elimination

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 10 4.1 Systems of Linear Equations in Two Variables Solving a System with Fractional Coefficients

11. 4.1 Systems of Linear Equations in Two Variables Some Special Systems Some systems of linear equations have no solution or an infinite number of solutions.

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 12 4.1 Systems of Linear Equations in Two Variables Some Special Systems

13. 4.1 Systems of Linear Equations in Two Variables Some Special Systems

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 14 4.1 Systems of Linear Equations in Two Variables Some Special Systems