Intro to systems_of_linear_equations
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Transcript of Intro to systems_of_linear_equations
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Systems of Linear Equations
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Solving Systems of Equations Graphically
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DefinitionsA system of linear equations is two or more linear equations whose solution we are trying to find.
(1) y = 4x – 6(2) y = – 2x
A solution to a system of equations is the ordered pair or pairs that satisfy all equations in the system.
The solution to the above system is (1, – 2).
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Solutions
Determine if (– 4, 16) is a solution to the system of equations.
y = – 4xy = – 2x + 8
(1) y = – 4x
16 = – 4(– 4)
16 = 16
(2) y = – 2x + 816 = – 2(– 4)
+ 816 = 8 + 8
16 = 16
Yes, it is a solution
Example:
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Solutions
Determine if (– 2, 3) is a solution to the system of equations.
x + 2y = 4y = 3x + 3
(1) x + 2y = 4– 2 + 2(3)
= 4– 2 + 6 =
44 = 4
(2) y = 3x + 3
3 = 3(– 2) + 3
3 = – 6 + 33 = – 3
But…
Example:
So it is NOT a solution
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Types of SystemsThe solution to a system of equations is the ordered pair (or pairs) common to all lines in the system when the system is graphed.
(– 4, 16) is the solution to the system.
y = – 4x
y = – 2x + 8
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Types of SystemsIf the lines intersect in exactly one point, the system has exactly one solution and is called a consistent system of equations.
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Types of SystemsIf the lines are parallel and do not intersect, the system has no solution and is called an inconsistent system.
y = 6x y = 6x – 5
There is no solution because the lines are parallel.
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Types of SystemsIf the two equations are actually the same and graph the same line, the system has an infinite number of solutions and is called a dependent system.
y = 0.5x + 4x – 2y = – 8There is an infinite number of solutions because each equation graphs the same line.