Download 3.0 Chapter 3 Packet

Name: _______________________________
Period: ________
Advanced Algebra 2 – Assignment Sheet
Chapter 3: Linear Systems and Matrices
HOMEWORK
Date
Section/Reading
Problem Sets
1.
2.
3.
3.1
Pages 153 – 155
3.1
Pages 152 & 159
3.2
Pages 160 – 163
4.
3.1 – 3.2
5.
Quiz 3.1 – 3.2
6.
7.
3.3
Pages 168 – 170
3.4
Pages 178 – 181
Pages 156 – 157; #17, 19, 20, 22, 23, 27, 28, 33, 35, 36
Page 152; #1 – 6 and Page 159; #1 – 8
Pages 164 – 165; #4, 5, 7, 10, 16, 18, 22, 23, 28, 31, 36, 39, 41, 43,
55, 56
Extra Practice 3.1 – 3.2
Read Section 3.3 on pages 168 – 170 and complete Guided Practice
problems 1, 3 and 4
Pages 171 – 172; #4, 8, 12, 13, 15, 21, 24, 25, 29, 30
Page 183; #25 – 30
Pages 183 – 185; #31, 32, 33, 35, 42
8.
3.4
9.
3.1 – 3.4
Page 1012; #1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14
10.
3.1 – 3.4
Extra Practice 3.1 – 3.4.
11.
Study Chapter 3
12.
Chapter 3 Test
Advanced Algebra 2
Name _________________________
Date ______________ Period _____
3.1 – Solve Linear Systems by Graphing – Day 1
System of two linear equations
Example 1: Graph the system of linear equations and estimate the solution. Then check the solution
algebraically.
4x  y  8
2 x  3 y  18
Classifying Systems –
Example 2: Solve each system by graphing and classify it as consistent and independent, consistent and
dependent or inconsistent.
a)
b)
2 x  5 y  10
4 x  10 y  20
3x  2 y  4
6 x  4 y  12
HW: Pages 156 – 157; #17, 19, 20, 22, 23, 27, 28, 33, 35, 36
Advanced Algebra 2
Name _________________________
Pages 156 – 157; #17, 19, 20, 22, 23, 27, 28, 33, 35, 36
Date ______________ Period _____
17)
19)
20)
22)
23)
27)
28)
33)
35)
36)
Advanced Algebra 2
Name _________________________
Date ______________ Period _____
3.1 – Solve Linear Systems by Graphing – Day 2
The graphing calculator can be used to solve systems of linear equations. Be sure the equations in the
system are in slope-intercept form (solved for y).
Press
Press
and enter the two equations into the calculator.
and then press
to see the table.
Use the arrow buttons to scroll up and down the table until the two y values are the same. The x and y
values of the point are the values where the tables match.
Another way to use the calculator to solve a system is by graphing both equations on the claculator and
finding the point of intersection. Be sure the equations in the system are in slope-intercept form (solved
for y).
Press
Press
and enter the two equations into the calculator.
to graph the equations.
Adjust the window using the
Press
and then
button until the point where the lines intersect is on the screen.
to open the calculate menu.
Select intersect (#5) from the menu and press enter.
Press enter at each of the three prompts.
The calculator will position the cursor at the point of intersection and display the x and y coordinates for
the solution.
Advanced Algebra 2
Name _________________________
Page 152; #1 – 6 and Page 159; #1 – 8
Date ______________ Period _____
1)
2)
3)
4)
5)
6)
Pages 159; #1 – 8
1)
2)
3)
4)
5)
6)
7)
8)
Advanced Algebra 2
Name _________________________
Date ______________ Period _____
3.2 – Solve Linear Systems Algebraically – Day 1
Substitution Method
1) Solve either equation for either variable.
2) Substitute the entire expression for the variable in the opposite equation and solve for the
remaining variable.
3) Substitute the value found in step two into either of the original equations and solve for the other
variable.
Example 1: Solve the system using the substitution method. Remember to check the solution.
4x  y  8
2 x  3 y  18
Elimination or Linear Combination Method
1) Multiply one or both equations by a constant to get opposite coefficients for either variable..
2) Add the revised equations to eliminate one variable and solve for the remaining variable.
3) Substitute the value found in step two into either of the original equations and solve for the other
variable.
Example 2: Solve the system using the elimination method.
2 x  5 y  11
3x  2 y  7
Example 3: Solve using either method.
2 x  5 y  10
4 x  10 y  20
Example 4: Solve using either method.
x  2y  4
2 x  4 y  12
Example 5: Find the coordinates of the point where the diagonals of the quadrilateral intersect.
HW: Pages 164 – 165; #4, 5, 7, 10, 16, 18, 22, 23, 28, 31, 36, 39, 41, 43, 55, 56
Advanced Algebra 2
Name _________________________
Pages 164 – 165;
Date ______________ Period _____
#4, 5, 7, 10, 16, 18, 22, 23, 28, 31, 36, 39,
41, 43, 55, 56
4)
5)
7)
10)
16)
18)
22)
23)
28)
31)
36)
39)
41)
43)
55)
56)
Advanced Algebra 2
Name _________________________
Extra Practice 3.1 – 3.2 – Page 167: 1 – 12
Date ______________ Period _____
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
Advanced Algebra 2
Name _________________________
Guided Practice 1, 3, & 4
Date ______________ Period _____
1)
3)
4)
Advanced Algebra 2
Name _________________________
Date ______________ Period _____
3.3 – Graph Systems of Linear Inequalities – Day 1
System of Linear Inequalities –
Graphing a System of Linear Inequalities
1) ______________________________________________________________________________
______________________________________________________________________________
2) ______________________________________________________________________________
______________________________________________________________________________
Example 1: Graph the system of inequalities.
x  y  3
6 x  y  1
x  3
Example 2: Graph the system of inequalities. y  7
4 x  5 y  20
Example 3: Graph the system of inequalities.
y  2
y  x2
HW: Pages 171 – 172; #4, 8, 12, 13, 15, 21, 24, 25, 29, 30.
Advanced Algebra 2
Name _________________________
Pages 171 – 172; #4, 8, 12, 13, 15, 21, 24, 25, 29, 30
Date ______________ Period _____
4)
8)
12)
13)
15)
21)
24)
25)
29)
30)
Advanced Algebra 2
Name _________________________
Date ______________ Period _____
3.4 – Solving Systems of Linear Equations in Three Variables – Day 1
Linear Equation in Three Variables –
SOLVING A SYSTEM OF LINEAR EQUATIONS IN THREE VARIABLES
1)
Choose two of the equations
2)
Apply the linear combination method to eliminate any one of the variables.
3)
Choose two of the original equations but not the same two used in Step 2.
4)
Apply the linear combination method to eliminate the same variable as in Step 3.
5)
Apply the linear combination to the equations from steps 3 and 5 to eliminate either of the
variables.
6)
Solve for the remaining variable.
7)
Substitute into the equation from step 3 or 5 to get the value of the second variable.
8)
Use any original equation to solve for the third variable.
9)
Write the answer as an ordered triple.
Example 1: Solve the system using the elimination method.
x yz 2
2x  2 y  2z  6
5 x  y  3z  8
Example 2: Solve the system using the elimination method.
3 x  y  2 z  10
6 x  2 y  z  2
x  4 y  3z  7
Example 3: Solve the system using the elimination method.
x yz 3
x yz 3
2x  2 y  z  6
Reminders:
 If any equation has a variable with a coefficient of 1, multiply this equation to eliminate the
variable from the other two equations.
 Double check each multiplication and check that all the signs are correct.
 Follow the pattern shown in the examples.
 There can be no solution, infinitely many solutions or exactly one solution written as an ordered
triple. Always check the solution in each of the equations.
HW: Page 183: #25 – 30
Advanced Algebra 2
Name _________________________
Page 183; #25 – 30
Date ______________ Period _____
25)
26)
27)
28)
29)
30)
Advanced Algebra 2
Name _________________________
Date ______________ Period _____
3.4 – Solving Systems of Linear Equations in Three Variables – Day 2
Warm Up:
Solve the system using the elimination method.
x  3y  7
2 x  6 y  4
Solve the system using substitution.
x  4 y  4
3x  2 y  5
Example 1 At the snack bar at a football game one hot dog, one pretzel and one soda costs $5.00. Two
hot dogs, one pretzel and two sodas costs $8.50 and three hot dogs, one pretzel and two sodas costs
$10.75. How much did each item cost individually?
SOLVING A SYSTEM OF LINEAR EQUATIONS IN THREE VARIABLES
1) Choose two of the equations
2) Apply the linear combination method to eliminate any one of the variables.
3) Choose two of the original equations but not the same two used in Step 2.
4) Apply the linear combination method to eliminate the same variable as in Step 3.
5) Apply the linear combination to the equations from steps 3 and 5 to eliminate either of the variables.
6) Solve for the remaining variable.
7) Substitute into the equation from step 3 or 5 to get the value of the second variable.
8) Use any original equation to solve for the third variable.
9) Write the answer as an ordered triple.
Reminders:
 If any equation has a variable with a coefficient of 1, multiply this equation to eliminate the
variable from the other two equations.
 Double check each multiplication and check that all the signs are correct.
 There can be no solution, infinitely many solutions or exactly one solution expressed as an
ordered triple. Always check the ordered pair in each of the equations.
HW: Pages 183 – 184: 31, 32, 33, 35, 42
Advanced Algebra 2
Name _________________________
Page 183; #31, 32, 33, 35, 42
Date ______________ Period _____
31)
32)
33)
35)
42)
Advanced Algebra 2
Name _________________________
Page 1012; #1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14
Date ______________ Period _____
1)
2)
4)
5)
6)
7)
8)
10)
11)
12)
13)
14)
Advanced Algebra 2
Name _________________________
Extra Practice 3.1 – 3.4
Date ______________ Period _____
1)
Solve the system by graphing.
x  2 y  4
3x  y  3
2)
Solve the system by graphing.
3x  6 y  12
x  2 y  3
3)
Solve the system algebraically.
3x  2 y  2
4x  3y  5
4)
Solve the system algebraically.
4 x  12 y  36
x  3y  9
5)
Graph the system of inequalities
2x  y  5
y  2 x 1
6)
Graph the system of inequalities
1
y  x2
3
y  3x  3
x  1
Solve the system.
3 x  y  z  2
7)
2 x  y  2 z  12
4x  2 y  z  1
8)
At a snack booth, one soda, one pretzel, and two hot dogs cost $7; two sodas, one pretzel, and two
hot dogs cost $8; and one soda and four hot dogs cost $10. What is the price (in dollars) of one hot
dog?