Chapter 3: Systems of Equations and Inequalities
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42 Terms
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Linear programming
________: the process of finding the max or min values of a function for a region defined by inequalities.
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Inconsistent
________: a system of equations that has no solutions.
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Vertex
________: a point on the boundary of a feasible region where two lines intersect.
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Constraints
________: the inequalities within the question.
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consistent system
Dependent: a(n) ________ with infinite solutions.
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Substitution method
________: one equation is solved for one variable in terms of the other, this expression is substituted for the variable in the other equation.
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Feasible region
________: the intersection of the graphs.
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Elimination method
________: eliminate one of the variables by adding to subtracting the equations.
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System of equations
________: two or more equations with the same variables.
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system of equations
two or more equations with the same variables
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consistent
a system of equations with at least one solution
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inconsistent
a system of equations that has no solutions
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independent
a consistent system with exactly one solution
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dependent
a consistent system with infinite solutions
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substitution method
one equation is solved for one variable in terms of the other, this expression is substituted for the variable in the other equation
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elimination method
eliminate one of the variables by adding to subtracting the equations
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system of inequalities
a set of inequalities, the solution set is represented by the intersection of the graphs of the inequalities
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constraints
the inequalities within the question
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feasible region
the intersection of the graphs
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bounded
when the graph of a system creates a polygonal region
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vertex
a point on the boundary of a feasible region where two lines intersect
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unbounded
when the graph of a system creates a region that is open
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linear programming
the process of finding the max or min values of a function for a region defined by inequalities
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ordered triple
(x, y, z)
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system of equations
two or more equations with the same variables
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consistent
a system with at least one solution
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inconsistent
a system that has no solutions
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independent
a consistent system with exactly one solution
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dependent
a consistent system with infinite solutions
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substitution
one equation is solved for one variable in terms of the other, this expression is substituted for the variable in the other equation
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elimination method
eliminate one of the variables by adding to subtracting the equations
32
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system of inequalities
two or more inequalities with the same variables
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constraints
the inequalities within the given problem
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feasible region
the intersection of the graphs
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bounded
when the graph of a system creates a polygonal region
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vertex
a point on the boundary of a feasible region where two lines intersect
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unbounded
when the graph of a system creates a region that is open
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linear programming
the process of finding the max or min values of a function for a region defined by inequalities
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three variable system with 1 solution
planes intersect at one point
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three variable system with infinite solutions
planes intersect in a line, planes intersect in the same plane
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three variable with no solution
the planes have no point in common
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ordered triple
(x, y, z)
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