HAA Chapter 3.1-3.4

Feasible Region

The area of the graph containing an infinite number of solutions to the system where all shading overlaps.

If the equations are parallel

No solution

calculator

graphs-equation-line-line standard find vertice where they intersect: hit menu-analyze graph- intersection- find point

solving by linear combination/elimination

1) multiply one or both equations by a number to get either the x's or y's to be opposites 2) add equations together. Solve 3) substitute the answer into either of the original equations. Solve (remember to add the two "c's" together)

solving by substitution

1) write the equations side by side 2) solve one of the equations for on of it's variables 3) substitute that equation into the other one. Solve 4) substitute that solution into the equation from step 2. Solve. *write final answer like this: (-8,5). Don't just show solved equations.

A system of linear equations

2 or more linear equations. The solution to the system is the ordered pair (x,y) that satisfies both equations, i.e. point of intersection. (x,y) has to satisfy BOTH EQUATIONS for it to be a solution

3.3 overview

Graph systems of linear inequalities (find the feasible region)

How to do word problems

Identify the variables first Then find the two equations Solve

If the equations are the exact same line on a graph

Infinitely many solutions

3.2 overview

Solving linear systems algebraically (substitution and elimination)

3.1 overview

Solving linear systems by graphing (no inequalities yet)

Bounded

a closed feasible region

Unbounded

an open feasible region

what way should y<x

below x, or down

y= |x+2| y=x

do the first one like an (h,k) problem: (-2, 0). Slope=1 plug in variables for the second one: (1,1), (2,2), (3,3), (4,4), etc.

what is this if your final answer: 0=0?

infinitely many solutions

Constraints

lines restricting the size of the feasible region

what is this if your final answer: 6=7?

no solution

y=3x+2 y=3x-2

no solution

0 greater than -2, true or false

true

automatic constraints

x≥0 y≥0

remember, inequality symbol flips if

you are dividing by a negative

when you get to D and E

you don't need to continue doing substitution