1. Systems of Linear Equations In Two Variables
5.1
Systems of Linear Equations
In Two Variables

2. 5.1 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.
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3. 5.1 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. 5.1 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.
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5. 5.1 Systems of Linear Equations in Two Variables
Possible Solutions for a Linear System of Two Variables
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6. 5.1 Systems of Linear Equations in Two Variables
The Substitution Method for Solving Systems
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7. 5.1 Systems of Linear Equations in Two Variables
Solving a System by Substitution

8. 5.1 Systems of Linear Equations in Two Variables
The Elimination Method for Solving Systems
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9. 5.1 Systems of Linear Equations in Two Variables
Solving a System by Elimination

10. 5.1 Systems of Linear Equations in Two Variables
Solving a System with Fractional Coefficients
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11. 5.1 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. 5.1 Systems of Linear Equations in Two Variables
Some Special Systems
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13. 5.1 Systems of Linear Equations in Two Variables
Some Special Systems

14. 5.1 Systems of Linear Equations in Two Variables
Some Special Systems
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