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Name:_______________________
College Algebra
Unit 1 – Standard 4
Day
Learning Target

1

2

3

4

5
6


7

8

Solve a 2 x 2 linear system of equations by
graphing
Solve a 2 x 2 linear system of equations by
substitution and elimination
Solve a 2 x 2 linear system of equations by
substitution and elimination
Solve a 3 x 3 linear system of equations by
elimination
Solve a 3 x 3 linear system of equations by
elimination
Perform basic operations on matrices
Solve a linear system of equations using
matrices
Use 2 x 2 linear systems of equations to model
and solve application problems
Use 3 x 3 linear systems of equations to model
and solve application problems
Assignment
Worksheet #1
Worksheet #2
Worksheet #3
Worksheet #4
Worksheet #5
Worksheet #6
Worksheet #7
Worksheet #8
Review
7
Review
8
Unit 1 – Standard 4 Test
9
This is an outline. The assignments/quizzes/tests are subject to change
College Algebra
Unit 1 – Standard 4
Linear Systems of Equations - Notes Day 1
Name_____________________
Learning Targets: Solve Systems of Equations by graphing.
Solve Systems of Equations with a graphing calculator.
Possible solutions when graphing two lines:
Consistent System
.Intersecting lines
Consistent System
Coinciding lines
Graph and solve the following system by hand.
 x  2 y  6
Ex 1. 
 5x  y  6
Ex 5.
Application
Inconsistent System
Parallel lines
Graph and solve the following systems by hand.
2x + y  5
Ex 2. 
 4 x  2y  6
Ex 5.
Application
3x  y  2
Ex 3. 
 y  5x – 2
To use the Nspire:
1.
2.
3.
4.
5.
6.
ASSIGNMENT #1: Worksheet #1
Graph the lines
Menu
Analyze graph (6)
Intersection (4)
Click left, click right
Find intersection point.
College Algebra
Unit 1 – Standard 4
Linear Systems of Equations - Notes Day 2
Name_____________________
Learning Targets: Solve Systems of Equations by Substitution
Solve Systems of Equations by Elimination
Warm Up:
Graph and solve the following system by hand.
2x + y  5
1. 
 4 x  2y  10
Ex 5.
Application
Elimination
2x + y  5
Ex. 1 
 4 x  6y  14
Substitution
 x + 2y  5
Ex 2. 
 xy  3
Your Choice
(Elimination or Substitution)
2x + y  5
Ex 3. 
 4 x  2y  8
ASSIGNMENT #2: Worksheet #2
ASSIGNMENT #3: Worksheet #3
College Algebra
Unit 1 – Standard 4
Linear Systems of Equations - Notes Day 4
Name_____________________
Learning Target: Solve Systems of Equations Containing 3 Variables
Consistent System
Infinite Number of Solutions
Ex 1.
x  2 y  z  9

 3 y  z  1

z4

Consistent System
One Solution
Ex 2.
 2x  y  z  3

 x  3 y  2 z  11
3x  2 y  4 z  1

Inconsistent System
No Solution
Ex. 3
2 x  y  2 z  8

 x  2 y  3z  9
 3x  y  4 z  3

ASSIGNMENT #4: Worksheet #4
ASSIGNMENT #5: Worksheet #5
College Algebra
Unit 1 – Standard 4
Linear Systems of Equations - Notes Day 6
Name_____________________
Learning Targets: Find the Sum and Difference of Two Matrices
Find Scalar Multiples of a Matrix
Find the Product of Two Matrix
Find the Inverse of a Matrix
Solve Systems of Equations Using Inverse Matrices
Column 1
Column 2
Column j
Column n
Row 1
Row 2
Row 3
Row 4
Rows by Columns
Identify the size of each matrix.
Ex 1.
Ex 2.
 3 7
A= 

  2 4
Ex 3.
 6 
B=  3 
 
  2
1 6  2 
C= 

 4 0  3
Add or subtract each matrix.
Ex 4.
Ex 5.
 4 2  3 7 
  3 9  +   2 4 =

 

5 6  1 1 6  2
3 7  9 - 4 0  3 =

 

Multiply each matrix by a scalar.
Ex 6.
Ex 7.
3A =
5B =
Calculator Problems:
You can multiply when the number of columns of the first matrix and the number of rows of the
second matrix match:
 3 7
3
 4  7
A= 
B=
C= 




  2 4
2
 1 2 
Ex 8. AB =
Ex 9.
BC =
Solve systems of equations using the calculator.
 3x  y  8
Ex 10. 
 2 x  y  4
ASSIGNMENT #6: Worksheet #6
 x yz 8

Ex 11. 2 x  3 y  z  2
3 x  2 y  9 z  9

College Algebra
Unit 1 – Standard 4
Linear Systems of Equations - Notes Day 7
Name_____________________
Learning Targets: Students will be able to use 2 x 2 linear systems of equations to model and solve
application problems
Steps in solving application problems using 2 x 2 linear systems
1) Determine the two unknowns you are being asked to find. These can usually be defined using the question at
the end of the problem.
2) Use variables to represent each of the unknowns.
3) Determine quantities for which you are given a total. Write equations for each of these total quantities. The
number of equations is always the same as the number of variables.
4) Solve the system of equations using matrices or the calculator.
Consumer Problems:
1) At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $2.35. One day, the receipts for a total of
172 cones and sundaes were $294.20. How many cones were sold?
Test Construction Problems:
2) Your teacher is giving you a test worth 100 points containing 40 questions. There are two‐point and four‐point
questions on the test. How many of each type of question are on the test?
Geometry Problems
3. A rectangular soccer field has perimeter 360 yd. Its length is 20 yd more than its width. What are its
dimensions?
ASSIGNMENT #7: Worksheet #7
College Algebra
Unit 1 – Standard 4
Linear Systems of Equations - Notes Day 8
Name_____________________
Learning Targets: Students will be able to use 3 x 3 linear systems of equations to model and solve
application problems
Steps in solving application problems using 3 x 3 linear systems
1) Determine the three unknowns you are being asked to find. These can usually be defined using the question at
the end of the problem.
2) Use variables to represent each of the unknowns.
3) Determine quantities for which you are given a total. Write equations for each of these total quantities. The
number of equations is always the same as the number of variables.
4) Solve the system of equations using matrices.
Mixture Problems
1) Experiments have shown that cars (C), trucks (T ), and buses (B) emit different amounts of air pollutants. In
one such experiment, a truck emitted 1.5 pounds (lb) of carbon dioxide (CO2) per passenger-mile and 2 grams
(g) of nitrogen oxide (NO) per passenger-mile. A car emitted 1.1 lb of CO2 per passenger-mile and 1.5 g of
NO per passenger-mile. A bus emitted 0.4 lb of CO2 per passenger-mile and 1.8 g of NO per
passenger-mile. A total of 85 mi was driven by the three vehicles, and 73.5 lb of CO2 and 149.5 g of NO were
collected. Use the following system of equations to determine the miles driven by each vehicle.
T  C  B  85.0
1.5T  1.1C  0.4B  73.5
2T  1.5C  1.8B  149.5
Geometry Problems
2) The measure of the largest angle of a triangle is 10° more than the sum of the measures of the other two angles
and 10° less than 3 times the measure of the smallest angle. Find the measures of the three angles of the
triangle.
Consumer Problems
3) A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of
278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10
less than twice the number of student tickets, how many of each type of ticket were sold for the showing?
ASSIGNMENT #8: Worksheet #8