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
