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4.1Systems of Linear Equations

A system of linear equations consists two or more linear equations.

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Systems of Linear Equations

7 5 62

3 2 10

x y

x y

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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.

, x y

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Solutions of a System of Linear Equations

1 1

4 5 3 2 14

Is a solution of ? 5, 24 3 14

2 1

x y

x y

4 3 14x y

20 6 14 5 4 1

2 1x y

14 14

5 2 2 1

5, 2 is a solution.

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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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Solving a System of Linear Equations Graphically

3 7

2 3 12

y x

x y

Solve the system graphically:

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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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One solution

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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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No Solution

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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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Infinite Solutions