slide 4.1- 1 4.1 systems of linear equations a system of linear equations consists two or more...
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Slide 4.1- 1
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
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