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Slide 4.1- 1 4.1 Systems of Linear Equations A system of linear equations consists two or more linear equations.

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Slide 4.1- 2 Systems of Linear Equations

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Slide 4.1- 3 Solutions of a System of Linear Equations A solution of a system of linear equations is an ordered pair that is a solution to each equation in the system.

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Slide 4.1- 4 Solutions of a System of Linear Equations Is a solution of ? is a solution.

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Slide 4.1- 5 Solving a System of Linear Equations Graphically To solve a system of linear equations graphically, begin by graphing each line. A solution of the system is an ordered pair that is on both lines.

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Slide 4.1- 6 Solving a System of Linear Equations Graphically Solve the system graphically:

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Slide 4.1- 7 One Solution Systems A system of equations that has a single ordered pair as its solution is called an independent system. Graphically, a system of linear equations is an independent system if the lines associated with the system intersect at a single point.

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Slide 4.1- 8 One solution

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Slide 4.1- 9 No Solution A system of equations that has no solution is called an inconsistent system. Graphically, a system of linear equations is an inconsistent system if the lines associated with the system are distinct parallel lines.

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Slide 4.1- 10 No Solution

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Slide 4.1- 11 Infinite Solutions A system of equations that has infinitely many solutions is called a dependent system. Graphically, a system of linear equations is a dependent system if the two lines associated with the system are actually the same line.

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Slide 4.1- 12 Infinite Solutions

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