Chapter 4 Review
NAME____________________________
Simplify each of the following completely by rewriting without parenthesis or negative
exponents.
1) 86  82
m8
4)
m3
7)
15 x 2 y 5
3x 4 y 5
2)
y 
5)
12m8
6m 3
8)
 4k  ak  3a k 
5 2
4
3)
 3a 
6)
y 
y 
9)
 7x y 
4 2
3
5
Write the equation of the line that passes through the given points.
10) (-3,-3) & (3,-7)
11) (-1,10) & (2,1)
Solve the following equations:
12) x  2 x  4   2 x  1 x  2
4
13)
8  x  2  2  2  x 
3 2
3
5 2
Directions: Solve the following system of equations by using the substitution method. Show
your work and check your answers.
14. y = x – 4
4x + y = 26
Solution: (_____,_____)
15. x = y + 4
2y + x = 19
Solution: (_____,_____)
16. x – 2y = 8
y = -4x + 5
Solution: (_____,_____)
17. 2x = 8
x+y=2
Solution: (_____,_____)
18. 2x + 3y = 31
y=x+7
Solution: (_____,_____)
Directions: Solve the following system of equations by using the elimination method. Show
your work and check your answers.
19. 3x + y = 6
-3x + 4y = 9
Solution: (_____,_____)
20. 2x – 3y = -16
X + 3y = 10
Solution: (_____,_____)
21. x + 2y = -3
x – 4y = 15
Solution: (_____,_____)
22. –x + 8y = 16
3x + 4y = 36
Solution: (_____,_____)
23. -2x + 3y = -11
2x – 4y = 14
Solution: (_____,_____)
Directions: Define your variables and write two equations that could be used to solve the
following problem. You do not need to actually solve the system.
24. Holmes Junior High School has x students. Harper Middle School has 125 fewer students
than Holmes. When the two schools are merged there will be 809 students. How many
students attend each school? Be sure to define your variables.
Let x = ___________________________________
Let y = ___________________________________
Equation #1: _______________________
Equation #2: _______________________
25. A one pound mixture of raisins and peanuts cost $7.50. The raisins cost $3.25 a pound and
the peanuts cost $5.75 a pound. How much of each ingredient is in the mixture? Be sure to
define your variables.
Let x = ___________________________________
Let y = ___________________________________
Equation #1: _______________________
Equation #2: _______________________
26. Katy weighs 105 pounds and is gaining 2 pounds per month. James weighs 175 pounds
and is losing 3 pounds a month. When will they weigh the same? Be sure to define your
variables.
Let x = ___________________________________
Let y = ___________________________________
Equation #1: _______________________
Equation #2: _______________________
27. The Ski Club is selling plates of cookies and cakes to raise money for their club expenses.
They decide charge $10 for each plate of cookies and $9.50 for each cake. The total
collected during the fund raiser was $218. If a total of 22 plates of cookies & cakes were
bought, then how many of each were sold during the fund raiser?
Let x = ___________________________________
Let y = ___________________________________
Equation #1: _______________________
Equation #2: _______________________
(1) 8 4
(2) y10
(3) 81a4
(8) 12a6 k 8
(9) 49x6 y10
(10) y  
(14) (6,2)
(15) (9,5)
(16) (2,-3)
(17) (4,-2)
(18) (2,9)
(19) (1,3)
(20) (-2,4)
(21) (3,-3)
(22) (8,-3)
(23) (1,-3)
(4) m5
2
x5
3
(5) 2m11
(11) y  3 x  7
(24) Let x = number of students that attend Holmes Junior HS
Let y = number of students that attend Harper Middle School
Equation #1: y = x – 125
Equation #2: x + y = 809
(25) Let x = number of pounds of raisins
Let y = number of pounds of peanuts
Equation #1: x + y = 1
Equation #2: 3.25x + 5.75y = 7.50
(26) Let x = number of months (time)
Let y = number of pounds (weight)
Equation #1: y = 105 + 2x
Equation #2: y = 175 – 3x
(27) Let x = number of plates of cookies sold
Let y = number of cakes sold
Equation #1: x + y = 22
Equation #2: 10x + 9.5y = 218
5
x2
(6) y 2
(7)
(12) x  2
(13) x  2