Algebra
Unit 2 Solving Equations and Inequalities
Name: ____________________________________________________________ Date: ________________________
Unit 2 Test Review
Find the solution of the linear system graphically. Write your solution in the blank provided.
_______1.
y  x  3
_______2.
y  x 1
y  2 x  7
3 x  6 y  12
Use substitution to solve the linear system. SHOW ALL WORK and write your solution in the space
provided.
y  2x  2
4 x  y  6
________3.
_______4.
6 x  2 y  16
y  2x  2
Use elimination to solve the linear system. SHOW ALL WORK and write your solution in the space
provided.
________5.
5x  3 y  7
_______6.
x  3y  5
3x  3 y  9
6x  2 y  2
Use any method to solve the linear system. SHOW ALL WORK and write your solution in the space
provided.
6 x  9 y  18
________7.
2 x  3 y  10
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Algebra
Unit 2 Solving Equations and Inequalities
Inequality Word Problems:
8. Bill wants to buy some CDs at the music store. Used ones sell for $4.99, and new ones sell for
$13.99. He has $75 to spend that he got for his birthday.
a) Write a linear inequality (not a system) to represent the situation. _______________________
b) Can Bill by 4 used and 4 new CDs? Explain why or why not. _____________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Systems of Linear Equations
9. A store sold 32 pairs of jeans for a total of $1050. Brand A sold for $30 per pair and Brand B sold for
$35 per pair.
a) Write a system of equations to represent the situation. ______________________ __________________
b) How many of Brand A were sold? __________________________
work:
10. You are selling tickets for a basketball game. Student tickets cost $3 and general admission tickets
cost $5. You sell 350 tickets and collect $1450.
a) Write a system of equations to represent the situation. ____________________ ____________________
b) How many of each type of ticket did you sell? ________________________________________________
work:
11. The football score for the home team’s last game was 27. They scored some field goals (worth 3
points each) and touchdowns (worth 7 points each – We are assuming they got all point after
touchdowns and did not go for any two point conversions) . They scored 5 times and only had
touchdowns or field goals.
a) Write a system of equations to represent the situation. _____________________ __________________
b) How many of each type did the team make? ________________________________________________
work:
12. The sum of the weights of my two dogs is 160 pounds. Sarge weighs three times more than Jojo.
a) Write a system of equations to represent the situation. _____________________ __________________
b) How much does each dog weigh? _________________________________________________________
work:
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Algebra
Unit 2 Solving Equations and Inequalities
Graph the systems of inequalities, and name one solution.
________13.
x  3 y  9
_______14. y   x  2
4 x  3 y  6
4 x  y  1
Systems of Linear Inequalities Word Problems:
15. Julia and Jackson are raising money for a Mother’s Day gift. They have a lemonade stand and
are selling cups of lemonade for $2 each and cookies for $1.50 each. They must raise at least $150.
a) Write an inequality to express the income from the lemonade stand. ________________________
b) They expect to sell at least 3 dozen cookies. Write an inequality to represent this situation.
_________________________
c) What is one solution for the system of inequalities? __________________ How do you know? ________
_________________________________________________________________________________________________
_________________________________________________________________________________________________
16. You are looking to buy a bouquet of flowers for your favorite math teacher. Lilies cost $3.00 each
and roses cost $4.00 each. You have budgeted no more than $24 to spend on flowers. You want to
buy at least 5 flowers.
a) Write a system of inequalities to represent the situation. __________________________
_________________________
b) Graph a system of inequalities to illustrate how many of each type of flower you can purchase if
you want to buy at least 5 flowers.
c) Explain how to use the graph to determine possible solutions.
____________________________________________________________________
____________________________________________________________________
d)What are the constraints?
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
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Algebra
Unit 2 Solving Equations and Inequalities
Equations and inequalities
17. Solve 3(2x + 5) = 8x – 5
18. Solve 4(2x – 4) = 5x + 3 + 3x
19. Solve, graph and write interval notation for the solution (Remember you will graph this on a
number line NOT a coordinate plane)
5x
 6  14
2
20. Solve, graph and write interval notation for the solution (Remember you will graph this on a
number line NOT a coordinate plane) 6 – 2x < -12
Explain: (To get full points for explanation problems, you must have complete sentences with details.)
21. Does every system of equations have exactly one solution? ____________ Why or why not? _______
_________________________________________________________________________________________________
_________________________________________________________________________________________________
22. Does every system of inequalities have a range of solutions? ___________________ Why or why
not? _________________________________________________________________________________________
______________________________________________________________________________________________
______________________________________________________________________________________________
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Algebra
Unit 2 Solving Equations and Inequalities
Sequences:
23. Write the recursive, explicit and function form of the sequence below. Then find the 100th term
and the sum of the first 100 terms.
6, 10, 14, 18…… A1 = ______________
d= ________________ n = __________________
Recursive: _____________________________________________
Explicit: _______________________________________
Function: ____________________________________
A100: _____________________________________
S100: _____________________________________
Linear or not? __________________
Type of sequence? _____________________
Functions, Domain and Range:
24. State the domain and range for the following graph. Use inequality and interval notation.
Domain inequality: ______________________________________
Domain Interval: _____________________________________
Range Inequality: _______________________________________
Range interval: _________________________________________
25. Given the function f(x) = 6x – 3, find f(-2).
f(-2) = _____________________
If f(x) = 3, what is x?
26. Solve for y:
2x – 5y = 30
27. Solve for y: -6x + 8y = 22
f(____) = 3
__________________________________
_________________________________
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