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Algebra 2 Notes
Section 3.1: Solve Linear Systems by Graphing
Objective(s):
Vocabulary:
I. System of Two Linear Equations:
(See Glossary p. 1080)
II. Solution of a System:
III. Consistent:
IV. Inconsistent:
V. Independent:
VI. Dependent:
Examples:
1. Graph the linear system and estimate the solution. Then check the solution algebraically.
5x – 2y = -10
2x – 4y = 12
2. Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent.
6x – 2y = 8
3x – y = 4
Notes 3.1 page 2
3. Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent.
-4x + y = 5
-4x + y = -2
4. A soccer league offers two options for membership plans. Option A includes an initial fee of $40 and costs $5 for each game
played. Option B costs $10 for each game played. After how many games will the total cost of the two options be the same?
Algebra 2 Notes
Section 3.2: Solve Linear Systems Algebraically
Objective(s):
Vocabulary:
I. Substitution Method:
Step 1:
Step 2:
Step 3:
*NOTE: Choose your variable in Step 1 wisely to make your work easier!
II. Elimination Method:
Step 1:
Step 2:
Step 3:
Examples:
1. Solve the system using the substitution method.
3x + 2y = 1
-2x + y = 4
2. Solve the system using the elimination method.
8x + 2y = 4
-2x + 3y = 13
Notes 3.2 page 2
3. Solve the linear system using any algebraic method.
a)
2x - 3y = 4
6x - 9y = 8
c)
8x + 9y = 15
5x – 2y = 17
b)
x–y=4
-6x + 6y = -24
d)
3x – 6y = 9
-4x + 7y = -16
4. At a pizza restaurant it costs $4 to make a small pizza that sells for $12, and it costs $6 to make a large pizza that sells
for $15. In one week, the restaurant spent a total of $1100 making pizzas and sold all of them for $2910. how many
small pizzas were sold?
Algebra 2 Notes
Section 3.3: Graph Systems of Linear Inequalities
Objective(s):
Vocabulary:
I. System of Linear Inequalities:
(See Glossary p. 1079)
II. Solution of a System of Inequalities:
III. Graph of a System of Inequalities:
III. Graphing a System of Linear Inequalities:
Step 1:
Step 2:
*NOTE: You may want to use colored pencils to distinguish the different half-planes.
Examples:
1. Graph the system of inequalities.
a)
y < 3x + 2
y > -x + 4
b)
4x + 2y > 8
y < -2x - 3
Notes 3.3 page 2
2. Graph the system of inequalities.
a)
y< 2
y > |x – 1|
b)
x > 10
x < 70
y>x
y
4
x  30
7
100
90
80
70
60
50
40
30
20
10
10
20
30 40
50 60
70 80 90 100
Algebra 2 Notes
Section 3.4: Solve Systems of Linear Equations in Three Variables
Objective(s):
Vocabulary:
I. Linear Equation in Three Variables:
II. System of Three Linear Equations:
(See Glossary p. 1079)
III. Solution of a System of Three Linear Equations:
I. Ordered Triple:
IV. Elimination Method for a Three-Variable System:
Step 1:
Step 2:
Step 3:
Note:
If you obtain a false equation, such as 0 = 1, in any of the steps, then the system
has
.
If you do not obtain a false equation, but obtain an identity such as 0 = 0, then the
system has
Examples:
1. Solve the system.
2x – y + 6z = -4
6x + 4y – 5z = -7
-4x – 2y + 5z = 9
.
Notes 3.4 page 2
2. Solve the system.
a)
x+y–z=2
3x + 3y – 3z = 8
2x – y + 4z = 7
b)
x+y+z=6
x–y+z=6
4x + y + 4z = 24
c)
3x + y – 2z = 10
6x – 2y + z = -2
x + 4y + 3z = 7
4. At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 sodas costs $13.35. A second order of
5 slices of pizza, 2 breadsticks, and 3 sodas costs $19.50. If four breadsticks and a soda cost $.30 more than a slice of pizza,
what is the cost of each item?