3-1 Solving Systems of Equations by Graphing

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

3-2 Solving Systems of Equations Algebraically

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

3-3 Solving Systems of Inequalities by Graphing

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

3-4 Linear Programming

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

Linear Programming Steps

1. define the variables

2. write a system of inequalities

3. graph the system of inequalities

4. find the coordinates of the vertices of the feasible region

5. write a linear function to be maximized or minimized

6. substitute the coordinates of the vertices into the function

7. select the greatest or least result; answer the question posed in the problem

3-5 Solving Systems of Equations in Three Variables

three variable system - 1 solution: planes intersect at one point

three variable system - infinite solutions: planes intersect in a line, planes intersect in the same plane

three variable system - no solution: the planes have no point in common

ordered triple: (x, y, z)