Algebra II C & S
Mr. Hornbeck
Chapter 3 Outline
Date
In-Class
Homework
Day 1
3-1
p. 142 #11, 12, 15, 16, 21, 22, 28, 31, 35-40, 43,45
Day 2
3-2
Day 3
Word Problems
3.1-3.2
Day 4
3.1, 3.2 WP Quiz
(long)
Day 5
3.3
Day 6
Finish 3.3 if needed
Start Ch 3 Review
p. 186-187 #1-3, 5-11
Ch 3 Word Problem Review
Day 7
Ch 3 Review
p. 189 #26-27 AND p. 943 #2-28 even
Day 8
Chapter 3
Practice Test
Day 9
Chapter 3 Test
p. 152 #11, 12, 16, 19, 23, 24, 27, 32, 34, 35,
40, 42, 46
WORKSHEET #1-12
p. 155 #1-19 all
p. 159 #16, 18, 20-26, 28, 31, 34, 39, 42, 47
Word Problems Due
3.1 Solving Linear Systems by Graphing
 System of Two Linear Equations: two equations written in Ax + By = C form
 Solution: an ordered pair that makes the two equations true
 One Solution = Intersecting Lines
 Infinite Solutions = Exactly Same Line
 No Solutions = Parallel Lines
Example 1: Checking Solutions of a Linear System
Check whether (a) (1,4) and (b) (-5,0) are solutions of the following system.
x – 3y = -5
-2x + 3y = 10
Step 1: Substitute both points into
each equation
Step 2: Determine whether a true
statement occurs
Step 1: Convert to y = mx + b form
Example 2: Solving a System Graphically
Solve the system.
2x – 2y = -8
2x + 2y = 4
Step 2: Graph each line
Step 3: Look for Intersections
Example 3: Systems with Many or No Solutions
Tell how many solutions the linear system has.
a) 2x + 4y = 12
x + 2y = 6
b)
x–y=5
2x – 2y = 9
3.2 Solving Linear Systems Algebraically
 Substitution Method: solve for either “x” or “y” in one equation and substitute into the
other equation
 Linear Combination Method: combine vertically in order to cancel out either the “x’s”
or the “y’s”
 May have to find opposite common multiples
 What would cancel out – 6?
Example 1: The Substitution Method
Solve using substitution method.
3x – y = 13
2x + 2y = -10
Example 2: Linear Combination Method
Solve using linear combination.
2x – 6y = 19
– 3x + 2y = 10
Step 1: Use the equation and solve
for “x” OR “y.”
Step 2: Sub in what “y” is for 2nd
equation
Step 3: After finding “x”, sub “x” back
into the equation from Step 2.
Step 1: Determine which letter to
cancel out
Step 2: Use common multiples to
cancel vertically
Step 3: Solve for the other letter
Step 4: Substitute that letter back
into either equation to find the letter
you canceled out
Example 3: Linear Combination or Substitution Method
Solve using one of the methods
–x + 2y = 3
4x – 5y = – 3
Example 4: Linear Combination or Substitution Method
Solve using one of the methods
3x – y = 4
–9x + 3y = –12
Example 5: Linear Combination or Substitution Method
Solve using one of the methods
6x – y = – 2
–18x + 3y = 4
3.3 Graphing and Solving Systems of Linear Inequalities
 System of Linear Inequalities: solve and graph like an equation, but shade one side of the
line. Where both lines overlap is your solution.
 <,> use dashed line
 ≤,≥ use solid line
Example 1: Graphing a System of Two Inequalities
Graph the system.
x – 2y ≤ 3
y > 3x – 4
Step 1: Convert to y = mx + b form
Step 2: Graph each line
Step 3: Shade each region lightly as
necessary and look for overlap
Example 2: Graphing a System of Three Inequalities
Graph the system.
Step 1: Convert.
x≤0
Step 2: Graph.
y≥0
Step 3: Shade lightly.
x – y ≥ -2
Step 4: Look for overlap.
Example 3: Graphing a System of Three Inequalities
Graph the system.
–x<y
X + 3y > 8