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Chapter 3Linear Systems
Section 1: Using Graphs and Tablesto Solve Linear Systems
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Objectives Solve systems of equations by using
graphs and tables. Classify systems of equations, and
determine the number of solutions.
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Vocabulary system of equations linear system consistent system inconsistent system independent system dependent system
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3.1: Using Graphs and Tablesto Solve Linear Systems
A system of equations is a set of two or more equations containing two or more variables.
A linear system is a system of equations containing only linear equations.
The solution of a system of equations is the set of all points that satisfy each equation.
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3.1: Using Graphs and Tablesto Solve Linear Systems
On the graph of the system of two equations, the solution is the set of points where the lines intersect.
A point is a solution to a system of equations if the x- and y-values of the point satisfy both equations.
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Example 1
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Example 2
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3.1: Using Graphs and Tablesto Solve Linear Systems
The systems of equations in Example 2 have exactly one solution.
However, linear systems may also have infinitely many or no solutions. A consistent system is a set of equations or inequalities that has at least one solution,
and an inconsistent system will have no solutions.
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3.1: Using Graphs and Tablesto Solve Linear Systems
You can classify linear systems by comparing the slopes and y-intercepts of the equations.
An independent system has equations with different slopes.
A dependent system has equations with equal slopes and equal y-intercepts.
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Example 3
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Example 4
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