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# c h a p t e r 5

### Systems

compound sentence A sentence in which two clauses are connected by the word and or by the word or
union the set consisting of those values in either one or both sets.
Addition Property of Inequality If a<b, then a+c < b+c
Multiplication of Properties Inequality If a < b and c > 0, then ac < bc. If a < b and c < 0, then ac > bc.
Linear Combination Method Involves adding multiples of the given equations.
System-Determinant Theorem A 2 X 2 system has exactly one solution if and only if the determinant of the coefficient matrix is NOT zero.
which side is the equation x > 5 shaded It is a dotted line shaded to the right
Feasible Set The set of solutions to a system of linear inequalities
Vertices It is the intersections of the boudaries (lines)
Linear-Programming Theorem The feasible region of every linear-programming problem is convex, and the maximum or minimum quantity is determined at one of the vertices of this feasible region.
Steps to solve a linear-programming problem 1. Identify variables 2. Identify the constraints 3. Graph system; find vertices of feasible set 4. Write a formula or an expression 5. Apply the Linear-Programming Theorem. 6. Interpret the results.
Created by: katelesperance