Section 3.2
Solving Linear Systems Algebraically
Algebraic methods to solving linear systems:
1. Substitution
2. Linear Combination (elimination)
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Hour_
* We still have the possibility of one, none,
or infinitely many solutions
Substitution solve one
Algebra II- Notes 3.4 Solving Systems of Linear Equations in
3 Variables
3.4 Solving Systems of Linear Equations in 3-Variables
System of three equation and three variables, (x, y, z) called an
ordered triple. Represents a system in three dimensional spac
Algebra II
1.7
Notes 1.7 & 2.7
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Solving Absolute Value Equations
Ex 1.
4
=?
Ex 5.
x 3
Ex 2.
=6
4
=?
Ex 3.
| x | = 5 so x = ?
Ex 4. | x | = -7 so x = ?
what could the value of x = ?
When solving you can rewrite the original as two linear equations
Ex
Algebra II
Notes 2.8 & 2.7ext
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2.8 Graphing Linear Inequalities
greater than
less than
less
than or equal
to
Dotted
Line
greater than or equal to
Solid Line
Steps to graphing linear inequalities:
1. Solve equation to slope intercept form and graph
Algebra II
Notes 2.1/2.2/2.3
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2.1 Relations and Functions
Definitions:
Relation a relation between two variables x and y is a set of ordered pairs. A relation could also be
a mapping or table of values.
Input/Domain the x-values in the relation
Outpu
Algebra II
Notes 2.4/3.1
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2.4 Writing the Equations of a Line
To find the slope: Given two points ( x1 , y1 ) and ( x 2 , y 2 ) , use the formula
y y1
m 2
x
x
2
1
Slope-Intercept Form:
Given the slope m and the y-intercept b, y = mx + b
Point-Slo
Algebra II
Notes 3.3 Ext. Linear Programming
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Many real life problems involve a process called optimization (finding the minimum or maximum
value of something). For example, a company may want to maximize profits. We will learn to find minimums
and m