copyright © 2010 pearson education, inc. all rights reserved sec 5.1 - 1 4.1 systems of linear...
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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1
4.1
Systems of Linear Equations
In Two Variables
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.
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.
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.
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
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
4.1 Systems of Linear Equations in Two Variables
Solving a System by Substitution
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
4.1 Systems of Linear Equations in Two Variables
Solving a System by Elimination
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
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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 12
4.1 Systems of Linear Equations in Two Variables
Some Special Systems
4.1 Systems of Linear Equations in Two Variables
Some Special Systems
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 14
4.1 Systems of Linear Equations in Two Variables
Some Special Systems