Unit 2 Solving Systems on equations by graphing

intersecting lines

one solution

unbounded region

open and can go on forever

substitution method

solve one equation for one variable then substitute the expression into other equation and solve, then substitute variable into other equation and solve

systems of equations

2 or more equations with the same variables (solution is an ordered pair)

linear programming

Method to find max and min values -- define variables. Write The inequalities. Graph the inequalities. Find the vertices. Develop a linear function. Find a maximum or minimum. Answer the problem in a sentence.

ordered triple

a solution to the system in which you solve for 3 variables (x, y, z)

bounded region

enclosed shape

graphing method

graphing the lines and finding where they intersect

constraints

inequalities (lines themselves)

same line

infinitely many solutions

Systems of linear inequalities

means finding the ordered pairs that satisfy all of the inequalities in that system. steps: Graph each inequality, shade appropriate region. Identify the region that is shaded for all of the inequalities. This is the solution to the system.

elimination method

multiply one or both equations by a number to result in 2 equations that have opposite terms. Add equations, eliminations one variable, solve. Substitute to solve for the variable

parallel lines

no solution

feasible region

the shaded area after the inequalities are graphed