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**Key Concepts**
A system of equations is a SET of equations.
A solution satisfies every equation in the set.
For two variables: x and y
. The 2 linear equations represent 2 lines in a plane.
Possible solutions:
. Graph: Two lines intersect at exactly one point.
Solution = intersection point (x, y).
System is called consistent.
Equations are called independent.
. Graph: Two parallel lines intersecting at no point.
No solution. Solution set = Ø.
System is called inconsistent.
Equations are called independent.
. Graph: Two lines overlap as the same line.
Solution = an infinite number of intersection points.
Write solution with one variable arbitrary.
System is called consistent.
Equations are called dependent.
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View Full Document Substitution Method:
. Isolate 1 variable in 1 equation.
. Substitute into 2nd equation.
Elimination Method:
. the coefficients of the eliminated variable in two
equations must be additive inverses
. multiply one or both equations by a number if needed
. add equations to eliminate one variable
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This note was uploaded on 08/30/2011 for the course MAC 1105 taught by Professor Staff during the Fall '08 term at University of Central Florida.
 Fall '08
 Staff
 Algebra, Linear Equations, Equations

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