Question 1

Solve the problem.
-Find two numbers whose sum is 40 and whose difference is 12.

Accepted Answer

A) 29 and 11 
B) 26 and 14 
C) 24 and 16 
D) 16 and 28 
A) 29 and 11 
B) 26 and 14 
C) 24 and 16 
D) 16 and 28

Question 2

Solve the problem.
-The perimeter of a rectangle is $78 \mathrm {~m}$. If the width were doubled and the length were increased by $12 \mathrm {~m}$, the perimeter would be $132 \mathrm {~m}$. What are the length and width of the rectangle?

Accepted Answer

A)  width $19 \mathrm {~m}$, length $19 \mathrm {~m}$ 
B)  width $14 \mathrm {~m}$, length $19 \mathrm {~m}$ 
C)  width $15 \mathrm {~m}$, length $24 \mathrm {~m}$ 
D)  width $24 \mathrm {~m}$, length $15 \mathrm {~m}$ 
A)  width $19 \mathrm {~m}$, length $19 \mathrm {~m}$ 
B)  width $14 \mathrm {~m}$, length $19 \mathrm {~m}$ 
C)  width $15 \mathrm {~m}$, length $24 \mathrm {~m}$ 
D)  width $24 \mathrm {~m}$, length $15 \mathrm {~m}$

Question 3

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { r } 
x - 3 y = 6 \
3 y + 1 = x
\end{array}$$

Accepted Answer

A)  Consistent and independent 
B)  Inconsistent and independent 
C)  Consistent and dependent 
D)  Inconsistent and dependent 
A)  Consistent and independent 
B)  Inconsistent and independent 
C)  Consistent and dependent 
D)  Inconsistent and dependent

Question 4

Solve using the elimination method.
-$$\begin{array} { l } 
- x - 3 y = - 2 \
- 5 x + 3 y = - 46
\end{array}$$

Accepted Answer

A)  $( 8 , - 2 )$ 
B)  No solution 
C)  $( 9 , - 3 )$ 
D)  $( 2,8 )$ 
A)  $( 8 , - 2 )$ 
B)  No solution 
C)  $( 9 , - 3 )$ 
D)  $( 2,8 )$

Question 5

Solve the problem.
-Andy has 33 coins made up of quarters and half dollars, and their total value is $\$ 13.25$. How many quarters does he have?

Accepted Answer

A)  18 quarters 
B)  22 quarters 
C)  20 quarters 
D)  13 quarters 
A)  18 quarters 
B)  22 quarters 
C)  20 quarters 
D)  13 quarters

Question 6

Solve the problem.
-The perimeter of a rectangle is $56 \mathrm {~cm}$. One side is $12 \mathrm {~cm}$ longer than the other side. Find the lengths of the sides.

Accepted Answer

A)  $8 \mathrm {~cm} , 20 \mathrm {~cm}$ 
B)  $11 \mathrm {~cm} , 23 \mathrm {~cm}$ 
C)  $8 \mathrm {~cm} , 12 \mathrm {~cm}$ 
D)  $16 \mathrm {~cm} , 28 \mathrm {~cm}$ 
A)  $8 \mathrm {~cm} , 20 \mathrm {~cm}$ 
B)  $11 \mathrm {~cm} , 23 \mathrm {~cm}$ 
C)  $8 \mathrm {~cm} , 12 \mathrm {~cm}$ 
D)  $16 \mathrm {~cm} , 28 \mathrm {~cm}$

Question 7

Solve the problem.
-Anne and Nancy use a metal alloy that is $16 \%$ copper to make jewelry. How many ounces of an alloy that is $10 \%$ copper must be mixed with an alloy that is $20 \%$ copper to form 55 ounces of the desired alloy?

Accepted Answer

A)  22 ounces 
B)  33 ounces 
C)  38 ounces 
D)  24 ounces 
A)  22 ounces 
B)  33 ounces 
C)  38 ounces 
D)  24 ounces

Question 8

Solve the system of equations by the elimination method.
-$$\begin{array} { l } 
- 7 x - 6 y = - 36 \
- 3 x + 4 y = 24
\end{array}$$

Accepted Answer

A)  no solution 
B)  $( 0,7 )$ 
C)  $( 0,6 )$ 
D)  $( - 1,7 )$ 
A)  no solution 
B)  $( 0,7 )$ 
C)  $( 0,6 )$ 
D)  $( - 1,7 )$

Question 9

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { c } 
x + y = 8 \
2 x - 2 y = 8
\end{array}$$

Accepted Answer

A)  Inconsistent and dependent 
B)  Consistent and dependent 
C)  Consistent and independent 
D)  Inconsistent and independent 
A)  Inconsistent and dependent 
B)  Consistent and dependent 
C)  Consistent and independent 
D)  Inconsistent and independent

Question 10

Solve the problem using the elimination method.
-A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $\$ 5.00$. Another customer buys 4 hot dogs and 3 bags of potato chips for $\$ 9.00$. Find the cost of each item.

Accepted Answer

A)  $\$ 1.75$ for a hot dog; $\$ 1.25$ for a bag of potato chips 
B)  $\$ 1.50$ for a hot dog; $\$ 1.25$ for a bag of potato chips 
C)  $\$ 1.00$ for a hot dog; $\$ 1.50$ for a bag of potato chips 
D)  $\$ 1.50$ for a hot dog; $\$ 1.00$ for a bag of potato chips 
A)  $\$ 1.75$ for a hot dog; $\$ 1.25$ for a bag of potato chips 
B)  $\$ 1.50$ for a hot dog; $\$ 1.25$ for a bag of potato chips 
C)  $\$ 1.00$ for a hot dog; $\$ 1.50$ for a bag of potato chips 
D)  $\$ 1.50$ for a hot dog; $\$ 1.00$ for a bag of potato chips

Question 11

Solve by the substitution method.
-$$\begin{array} { l } 
x - 5 y = - 27 \
- 6 x - 6 y = - 90
\end{array}$$

Accepted Answer

A)  No solution 
B)  $( - 8,8 )$ 
C)  $( 7,8 )$ 
D)  $( 8,7 )$ 
A)  No solution 
B)  $( - 8,8 )$ 
C)  $( 7,8 )$ 
D)  $( 8,7 )$

Solve the problem. -Find two numbers whose sum is 40 and whose difference is 12.

Solve the problem. -The perimeter of a rectangle is $78 \mathrm {~m}$ . If the width were doubled and the length were increased by $12 \mathrm {~m}$ , the perimeter would be $132 \mathrm {~m}$ . What are the length and width of the rectangle?

Classify the system as consistent or inconsistent, and dependent or independent. - x-3y=6 3y+1=x

Solve using the elimination method. - -x-3y=-2 -5x+3y=-46

Solve the problem. -Andy has 33 coins made up of quarters and half dollars, and their total value is $\$ 13.25$ . How many quarters does he have?

Solve the problem. -The perimeter of a rectangle is $56 \mathrm {~cm}$ . One side is $12 \mathrm {~cm}$ longer than the other side. Find the lengths of the sides.

Solve the problem. -Anne and Nancy use a metal alloy that is $16 \%$ copper to make jewelry. How many ounces of an alloy that is $10 \%$ copper must be mixed with an alloy that is $20 \%$ copper to form 55 ounces of the desired alloy?

Solve the system of equations by the elimination method. - -7x-6y=-36 -3x+4y=24

Classify the system as consistent or inconsistent, and dependent or independent. - x+y=8 2x-2y=8

Solve the problem using the elimination method. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $\$ 5.00$ . Another customer buys 4 hot dogs and 3 bags of potato chips for $\$ 9.00$ . Find the cost of each item.

Solve by the substitution method. - x-5y=-27 -6x-6y=-90

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

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Exam 8: Systems of Equations