Algebra 1
Chapter 4 Review
1. Given the following two clues, show all four representations (tile pattern, table, rule, graph) of the pattern.
Write a few sentences explaining how you figured out the pattern.
x
y
0
1
2
3
4
5
6
7
Figure #5
2. Explain the steps required to solve the equation shown on the equation mat below. Solve the equation and be
sure to show all of your steps.
+
x
x x2
–
x
x
x
x
x2
x
x
x
+
–
3. MacKensie solved the following equation showing all of her steps. Estefan, a member of her group, thinks
that there is an error. Who is correct? Explain how you know. If Estefan is correct, then explain MacKensie’s
mistake and make changes to solve the problem correctly.
2(y  1)  2  4  2y  y
2y  2  2  4  y
2y  4  y
2y  y  4  y  y
2
4. Adrian is in Algebra 2. He solved the equation 2x  5x 13  20 and got the answer x  3 , but he’s not
feeling very confident. Decide whether or not he is correct and convince him of your position.
5. Solve this system of equations:
6. Solve this system of equations:
7. Solve this system of equations:
3x  5y  15
4x  5y  6
y  2x 1
4 x  3y  7
0.45 x  0.65 y  15.35
9x  13y  305
8. Solve this system of equations:
8 x  3y  18
5 x  1.875 y  11.25
9. If 3x  y  8 is one equation in a system of equations, and the system has infinitely solutions, what is the
other equation? Is there more than one answer? Explain.
10. Gabby solved this system of equations:
y  15 x  15
3x  6y  15
She found the solution to be (25, -10). Is Gabby correct? How do you know? Be clear and complete!
11. Wendi, a new student, is trying to understand all of the connections and relationships between
representations of patterns. She does not see how the figure below is connected to the graph. Explain the
connection to her.
y
Number
of Tiles
12
3
9
6
3
x
1 2 3 4
Figure
Number
12. Alex dumped out his piggy bank and there were only nickels, dimes, and quarters. There were three times
as many dimes as nickels, and 40 more quarters than nickels. If the total amount of money was $17.20, how
many of each type of coin were there?
13. Dominic is helping his friend solve systems of equations. He wants to give her a problem to practice that
has two lines intersecting at the point (3, 2). Write a system of equations that will have (3, 2) as a solution and
demonstrate how to solve it. Think about graphing a couple of lines if you are stuck.
14. Examine the following systems of equations. Decide for each system which method would be the most
efficient, convenient, and accurate: graphing, substitution, elimination, or the equal values method. Justify your
reasons for choosing one strategy over the others. Then solve each system.
a.
x  2y  6
x  3  4y
b.
x4y
y  3x  4
c.
a  b  10
3a  4b  6
15. Dorothy is thinking of two numbers. The sum of the two numbers is 40 and the difference is 6. Write a
system of equations and use the elimination method to find the two numbers. Write your solution as an ordered
pair.
16. A system of equations is represented on the two equation mats below.
+
x
+
y
x
+
x
x
–
–
x
x
+
y
x
–
–
a.
Write the system using algebraic sentences.
b.
Merge the two equation mats, simplify, and solve.
c.
Use your solution for x in part (b) to find y.
d.
Does your solution in part (c) (x, y) solve the system you wrote in part (a)?
17. Solve each equation below.
a. 2.5 
x
5
b.
4
9
x
 10
c.
x
1

2 x1
100
d.
5 x
9

2
3
18. Pearl solved a system of equations using substitution. Did she do it correctly? How do you know? If she
did not, find her error and solve the system correctly.
Pearl’s Solution:
System: {
𝑦 = −5 − 𝑥
2𝑥 + 𝑦 = 20
2x  (5  x)  20
x  5  20
x  5  5  20  5
x  25
x  25 y  30
Write and solve a system of equations for each situation.
19. The cost for 20 blank recordable CDs and 6 music CDs is $80.70. The cost of 30 blank recordable CDs and
4 music CDs is $66.30. Find the cost of each blank recordable CD and each music CD.
20. A hot air balloon is 15 ft above the ground and is rising at a rate of 10 ft per minute. Another balloon is 165
ft above the ground and is descending at a rate of 15 ft per minute. At what height will the balloons be the same
distance from the ground?
21. The drama club sold t-shirts and baseball caps in a fund-raiser. The t-shirts sold for $12, and the caps sold
for $9. The club sold a total of 114 shirts and caps. If the club raised $1242, how many t-shirts and how many
caps were sold?
22. Adult tickets to the school musical are $5 and student tickets are $2. There are 300 seats in the auditorium
where the musical will be performed. The ticket sale for one performance is $900. How many of each type of
ticket were sold?
23. Alvira wants to sign up for cell phone service. She’s trying to decide which company she should choose.
Telecorp has a flat rate of 7 cents per minute, Americall charges 25 cents per call and 3 cents per minute, and
Phonebusters charges 35 cents per call and 2 cents per minute.
a. Represent each phone plan with a table and a rule (equation).
b. Graph each plan on the same set of axes, where x represents the time in minutes and y represents the
cost of the call in cents. Use different colors to represent the different phone plans.
c. How long will a call need to be to cost the same for Americall and Phonebusters? What about
Telecorp and Phonebusters? ______________________ __________________________
d. If Alvira makes calls that last a very long time, which plan should she choose? Why? Show how
your graph confirms this. _______________________________________________________________
____________________________________________________________________________________
e. If Alvira makes lots of very short calls, which plan should she choose? Why? Show how your graph
confirms this. ________________________________________________________________________
___________________________________________________________________________________
Solve each for the indicated variable.
24.
x  yz  w for w
25.
27.
ab
 d  4 for b
c
28. 2m  3  n for m
b  c  de
for d
26.
gh  i  j
Solve each equation. Be sure to check your solutions.
29.  47  x   3
30. x  5  3  6
31. x  6  11
32.  28  x  4  4
33. 1 x  4  6
34. x  8  6  8
35. 2 5x  1  8  16
36. 3x  9  2  7
3
5
Simplify completely leaving no negative exponents.
3x y 
1 3
2
37.
3
18 x y
2
(3x) 3 x 2 y 2
40.
 4 .
3y3
x
 4a b
5
38.
2
39.  2r 5 s   3rs 2 
2
0 2
2a b
  5d 2 f 6 

41. 
3 
 10df 
2
42.
5 x3 y 4
5x  y
2 2
1
3
for h
Answers:
1. [ y  x 10 ]
2. [ x  4 ]
3. [MacKensie is correct. Substituting 4 for y in the original equation works. ]
4. [Yes, it is a solution. Justifications vary. ]
5. [ (3, 6/5) ]
6. [(1, 1) ]
7. [No solution. ]
8. [Infinitely many solutions. ]
9. [There are many possible answers! The easiest way to find an equation is to write a multiple of the original
equation: -3kx + ky = 8k where k ≠ 0, 1 because if k = 1 it would be the same equation. ]
10. [Yes, she is. Students can verify this by either solving the system or plugging the point into BOTH
equations and showing that it results in a true statement.]
11. [ The graph represents the equation y  3x  3 . Figure 3 has 12 tiles, which is consistent with the graph
and equation. Students could mention that the graph shows a growth rate of 3 new tiles for each new figure,
which matches the 3 shaded tiles in the figure. ]
12. [ 12 nickels, 36 dimes, and 52 quarters ]
13. [ Answers will vary. Accept all systems that have (3, 2) as a solution. ]
14. [ Answers vary, but generally, a is easiest with equal values, b with substitution and c with elimination or
substitution ]
15. [ x  y  40, x  y  6 ; (23, 17) ]
16. [ a: 2x  y  10 , 5x  y  18 , b: x  4 , c: y  2 , d: yes ]
1
17. [ a: 12.5, b: 40
, c: 98
, d: –1 ]
9
18. [ Yes. The ordered pair at the end does solve both equations. ]
20𝑥 + 6𝑦 = 80.70
19. {
Blank = $.75 Music = $10.95
30𝑥 + 47 − 66.30
𝑦 = 15 + 10𝑥
20. {
The balloons will meet at 75 ft
𝑦 = 165 − 15𝑥
12𝑡 + 9𝑐 = 1242
21. {
72 t-shirts and 42 caps
𝑡 + 𝑐 = 114
5𝑥 + 2𝑦 = 900
100 adult tickets and 200 students tickets
𝑥 + 𝑦 = 300
23. a.
x 0 1 2 3 4 5 6 7 8 9 10 11 12
T 0 7 14 21 28 35 42 49 56 63 70 77 84
A 25 28 31 34 37 40 43 46 49 52 55 58 61
P 35 37 39 41 43 45 47 49 51 53 55 57 59
22. {
T: 𝑦 = 7𝑥
A: 𝑦 = 25 + 3𝑥
c. [10 min; 7 min]
P: 𝑦 = 35 + 2𝑥
d. [Phonebusters. It costs more for short calls (up to 7 min) but is cheapest after 10 min]
e. [Telecorp. It is least expensive for calls less than 7 min]
24. −𝑥 + 𝑦𝑧 = 𝑤
28. 𝑚 =
𝑛−3
32. 𝑥 = 12 𝑜𝑟 4
36. 𝑥 =
39.
−27𝑠4
4𝑟 7
3
𝑜𝑟
𝑏−𝑐
𝑒
29. 𝑥 =
2
14
25.
4
3
=𝑑
31
4
𝑜𝑟
26. ℎ =
25
4
33. No Solution
37.
40.
3𝑥 3
2𝑦
1
81𝑥𝑦
𝑗+𝑖
𝑔
27. 𝑏 =
𝑐(𝑑−4)
𝑎
30. 𝑥 = 8 𝑜𝑟 2
31. 𝑥 = 5 𝑜𝑟 − 5
34. 𝑥 = 10 𝑜𝑟 6
35. 𝑥 =
38.
41.
1
32𝑎10 𝑏 4
𝑑2 𝑓 6
4
42.
𝑦5
5𝑥
11
5
𝑜𝑟 −
13
5