Chapter 3: Systems of Equations and Inequalities

Linear programming

________: the process of finding the max or min values of a function for a region defined by inequalities.

Inconsistent

________: a system of equations that has no solutions.

Vertex

________: a point on the boundary of a feasible region where two lines intersect.

Constraints

________: the inequalities within the question.

consistent system

Dependent: a(n) ________ with infinite solutions.

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.

Feasible region

________: the intersection of the graphs.

Elimination method

________: eliminate one of the variables by adding to subtracting the equations.

System of equations

________: two or more equations with the same variables.

system of equations

two or more equations with the same variables

consistent

a system of equations with at least one solution

inconsistent

a system of equations that has no solutions

independent

a consistent system with exactly one solution

dependent

a consistent system with infinite solutions

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

elimination method

eliminate one of the variables by adding to subtracting the equations

system of inequalities

a set of inequalities, the solution set is represented by the intersection of the graphs of the inequalities

constraints

the inequalities within the question

feasible region

the intersection of the graphs

bounded

when the graph of a system creates a polygonal region

vertex

a point on the boundary of a feasible region where two lines intersect

unbounded

when the graph of a system creates a region that is open

linear programming

the process of finding the max or min values of a function for a region defined by inequalities

ordered triple

(x, y, z)

system of equations

two or more equations with the same variables

consistent

a system with at least one solution

inconsistent

a system that has no solutions

independent

a consistent system with exactly one solution

dependent

a consistent system with infinite solutions

substitution

one equation is solved for one variable in terms of the other, this expression is substituted for the variable in the other equation

elimination method

eliminate one of the variables by adding to subtracting the equations

system of inequalities

two or more inequalities with the same variables

constraints

the inequalities within the given problem

feasible region

the intersection of the graphs

bounded

when the graph of a system creates a polygonal region

vertex

a point on the boundary of a feasible region where two lines intersect

unbounded

when the graph of a system creates a region that is open

linear programming

the process of finding the max or min values of a function for a region defined by inequalities

three variable system with 1 solution

planes intersect at one point

three variable system with infinite solutions

planes intersect in a line, planes intersect in the same plane

three variable with no solution

the planes have no point in common

ordered triple

(x, y, z)