Download - Assignment 9.2: Graphing Exponential Decay
Algebra 2 Name______________________________ ALT 09
Assignment 9.2: Graphing Exponential Decay
Determine whether each function represents growth or decay.
1. 𝑓(𝑥) = &'()* 2. 𝑓(𝑥) = +
,(3*) 3. 𝑓(𝑥) = &.
')* 4. 𝑓(𝑥) = (0.8)*
Match the function with its graph.
5. 𝑓(𝑥) = &+,)* 6. 𝑓(𝑥) = −&+
,)* 7. 𝑓(𝑥) = 3 &+
,)*
8. 𝑓(𝑥) = +
'&+,)* 9. 𝑓(𝑥) = −3 &+
,)* 10. 𝑓(𝑥) = −+
'&+,)*
Depreciation: You buy a new computer and accessories for $1200. The value of the computer decreases by 30% each year. 11. Write an exponential decay model giving the computer’s value V (in dollars) after t years. 12. What is the value of the computer after 4 years?
Graph each equation. 13. 𝑓(𝑥) = &,
')* 14. 𝑓(𝑥) = 2 • &+
,)*
D: R: D: R: 15. 𝑓(𝑥) = −(0.25)* 16. 𝑓(𝑥) = &+
')*+ 2
D: R: D: R: 17. 𝑓(𝑥) = (0.5)*8+ 18. 𝑓(𝑥) = &+
,)*9,
− 1 D: R: D: R:
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 73x + y = 6!"#
2. x − 5y = −53x −15y = 9"#$
3. x + y = 42x − y = 6"#$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12−2x + y = −4"#$
5. x + 2y =114x +3y = 9!"#
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 73x + y = 6!"#
2. x − 5y = −53x −15y = 9"#$
3. x + y = 42x − y = 6"#$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12−2x + y = −4"#$
5. x + 2y =114x +3y = 9!"#
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 73x + y = 6!"#
2. x − 5y = −53x −15y = 9"#$
3. x + y = 42x − y = 6"#$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12−2x + y = −4"#$
5. x + 2y =114x +3y = 9!"#
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 73x + y = 6!"#
2. x − 5y = −53x −15y = 9"#$
3. x + y = 42x − y = 6"#$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12−2x + y = −4"#$
5. x + 2y =114x +3y = 9!"#
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 73x + y = 6!"#
2. x − 5y = −53x −15y = 9"#$
3. x + y = 42x − y = 6"#$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12−2x + y = −4"#$
5. x + 2y =114x +3y = 9!"#
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 73x + y = 6!"#
2. x − 5y = −53x −15y = 9"#$
3. x + y = 42x − y = 6"#$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12−2x + y = −4"#$
5. x + 2y =114x +3y = 9!"#
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
(x+ 2y = 7
3x+ y = 62.
(x� 5y = �5
3x� 15y = 93.
(y = 2|x� 3|� 4
y = x� 1
x
y
�10 10
�10
10
x
y
�10 10
�10
10
x
y
�10 10
�10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
(6x� 3y = 12
�2x+ y = �45.
(x+ 2y = 11
4x+ 3y = 9
6.
(15x+ 2y = 4
3
x+ 23y = 2
7.
(0.5x� 0.3y = 1.3
�1.4x+ 1.2y = �2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
(6x+ 12y = �7
x+ 2y = 29.
(5x+ 4y = �3
3x� 7y = 17
10.
(43x+ 6y = �1
4x� 4y = 133
11.
(0.3x� 0.2y = 1.4
0.12x� 0.8y = 0.56
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3