16 terms

Expression

a mathematical phrase that combines numbers and/or variables using mathematical operations.

Equation

a mathematical sentence that shows that two expressions are equivalent (=).

Linear equation

an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

Function

a relation from a set of inputs (x) to a set of possible outputs (y); where each input is related to exactly one output.

Linear function

a function whose graph is a straight line.

Inequality

a mathematical sentence that shows that two expressions are not equivalent.

System of equations

a collection of two or more equations with the same set of variables.

System of inequalities

a collection of two or more inequalities with the same set of variables.

Solution to systems of equations

the ordered pair that satisfies all equations in the system.

Methods for solving a system of equations

graphing, substitution, and elimination

Parallel lines

lines in the same plane that do not intersect; their slopes are the same, m1 = m2, and their y intercepts are different.

Perpendicular lines

lines that intersect to form right angles; their slopes are opposite reciprocals.

Linear programming

a mathematical procedure to find values of variables that satisfy a set of linear constraints and optimize the value of a linear objective function.

Objective function

an algebraic expression like 7x - 3y whose value is to be optimized within the constraints of the problem.

Constraints

limitations on values that variables may assume in a problem situation.

Feasible region

the area of the graph in which every point satisfies the constraint inequalities.