Systems of Equations

Elimination:
You can add the two equations together, so if there is a negative and positive number that is the same but opposite they can cancel out and you can find the first value

Substitution:
You can find out what value one of the variables has, by just solving for that one variable, and then substitute it with what you found.

Graphs of linear equations may be related to each 
other in one of three ways. 
Exactly one common point 
One solution 
Consistent 
Independent 
Parallel lines 
No common points 
No solution 
Inconsistent 
Independent 
Lines are identical. 
Infinitely many common points 
Infinitely many solutions 
Consistent 
Dependent
1) 
One solution: planes 
intersect in exactly 
One point. 
(2) 
No solution: three planes; 
each intersects another; at 
no point do all intersect. 
No solution: 
parallel planes. 
Infinitely many solutions: 
planes intersect in a line. 
Infinitely many solutions: 
planes are identical.

Systems of Inequalities

Where the inequalities overlap is where the system is true

Maximize *Equation* subject to *2nd Equation* questions:
Ex.

5y subject to 
x + yS3 
x 20 
Maxi mum

Other example:

5 " 谷 「 当 す 、 3 ) 、 22 〔 準 「 D

Nonlinear Systems and Inequalities:
There might be multiple x and y-values
Usually, use substitution
Ex. quadratic functions will obviously sometimes have 2 solutions

Feasible area:
Where the two or more inequalities overlap