Question 1

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { l } 
4 x + 4 y = 1 \
8 x + 8 y = 2
\end{array}$$

Accepted Answer

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

Question 2

Solve the problem using the elimination method.
-In a right triangle, one acute angle is $54 ^ { \circ }$ more than twice the other. Find each acute angle.

Accepted Answer

A)  $12 ^ { \circ }$ and $78 ^ { \circ }$ 
B)  $37 ^ { \circ }$ and $53 ^ { \circ }$ 
C)  $21 ^ { \circ }$ and $69 ^ { \circ }$ 
D)  $28 ^ { \circ }$ and $62 ^ { \circ }$ 
A)  $12 ^ { \circ }$ and $78 ^ { \circ }$ 
B)  $37 ^ { \circ }$ and $53 ^ { \circ }$ 
C)  $21 ^ { \circ }$ and $69 ^ { \circ }$ 
D)  $28 ^ { \circ }$ and $62 ^ { \circ }$ A

Question 3

Solve by the substitution method.
-$$\begin{array} { c } 
7 x + 9 y = - 54 \
- 3 x - 4 y = 24
\end{array}$$

Accepted Answer

A)  $( - 1 , - 5 )$ 
B)  $( 0 , - 5 )$ 
C)  No solution 
D)  $( 0 , - 6 )$ 
A)  $( - 1 , - 5 )$ 
B)  $( 0 , - 5 )$ 
C)  No solution 
D)  $( 0 , - 6 )$ D

Question 4

Solve by the substitution method.
-$$\begin{array} { l } 
8 x + 8 y = - 32 \
5 x - 4 y = - 20
\end{array}$$

Accepted Answer

A)  $( - 5,1 )$ 
B)  No solution 
C)  $( - 4,0 )$ 
D)  $( - 4,1 )$ 
A)  $( - 5,1 )$ 
B)  No solution 
C)  $( - 4,0 )$ 
D)  $( - 4,1 )$

Question 5

Solve.
-A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5 mph slower than the power boat. Find the speed of each boat.

Accepted Answer

A) Power boat travels 10 mph and cruiser travels 5 mph. 
B) Power boat travels 20 mph and cruiser travels 15 mph. 
C) Power boat travels 15 mph and cruiser travels 10 mph. 
D) Cannot be determined with information given. 
A) Power boat travels 10 mph and cruiser travels 5 mph. 
B) Power boat travels 20 mph and cruiser travels 15 mph. 
C) Power boat travels 15 mph and cruiser travels 10 mph. 
D) Cannot be determined with information given.

Question 6

Solve the system of equations by the elimination method.
-$$\begin{array} { l } 
3 x - 5 y = 2 \
18 x - 30 y = 12
\end{array}$$

Accepted Answer

A)  $( 6 , - 10 )$ 
B)  infinitely many solutions 
C)  $( - 10,6 )$ 
D)  no solution 
A)  $( 6 , - 10 )$ 
B)  infinitely many solutions 
C)  $( - 10,6 )$ 
D)  no solution

Question 7

Solve.
-Jill is 27.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2.5 kilometers per hour. They meet in 5 hours. How fast is Joe walking?

Accepted Answer

A) 2.5 kilometers per hour 
B) 3 kilometers per hour 
C) 5 kilometers per hour 
D) 4 kilometers per hour 
A) 2.5 kilometers per hour 
B) 3 kilometers per hour 
C) 5 kilometers per hour 
D) 4 kilometers per hour

Question 8

Solve.
-An express and local train leave GraysLake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Accepted Answer

A)  Express's rate $= 50 \mathrm { mph }$ and local's rate $= 25 \mathrm { mph }$. 
B)  Express's rate $= 25 \mathrm { mph }$ and local's rate $= 12.5 \mathrm { mph }$. 
C)  Express's rate $= 60 \mathrm { mph }$ and local's rate $= 30 \mathrm { mph }$. 
D)  Cannot be determined with information given. 
A)  Express's rate $= 50 \mathrm { mph }$ and local's rate $= 25 \mathrm { mph }$. 
B)  Express's rate $= 25 \mathrm { mph }$ and local's rate $= 12.5 \mathrm { mph }$. 
C)  Express's rate $= 60 \mathrm { mph }$ and local's rate $= 30 \mathrm { mph }$. 
D)  Cannot be determined with information given.

Question 9

Solve.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 7 miles per hour, and Delvis is traveling at the speed of 4 miles per hour. In 2 hours what is the distance between them?

Accepted Answer

A) 3 miles 
B) 15 miles 
C) 6 miles 
D) 7 miles 
A) 3 miles 
B) 15 miles 
C) 6 miles 
D) 7 miles

Question 10

Solve the problem using the elimination method.
-Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 81$ for 3 days and 300 miles, while Mary was charged $\$ 145$ for 5 days and 600 miles. What does Best Rental charge per day and per mile?

Accepted Answer

A)  $\$ 18$ per day and $11 \nsubseteq$ per mile 
B)  $\$ 10$ per day and $17 \nsubseteq 5$ per mile 
C)  $\$ 16$ per day and $11 \nsubseteq \subset$ per mile 
D)  $\$ 17$ per day and $10 \simeq$ per mile 
A)  $\$ 18$ per day and $11 \nsubseteq$ per mile 
B)  $\$ 10$ per day and $17 \nsubseteq 5$ per mile 
C)  $\$ 16$ per day and $11 \nsubseteq \subset$ per mile 
D)  $\$ 17$ per day and $10 \simeq$ per mile

Question 11

Solve the problem.
-Walt made an extra $\$ 10,000$ last year from a part-time job. He invested part of the money at $10 \%$ and the rest at $9 \%$. He made a total of $\$ 960$ in interest. How much was invested at $9 \%$ ?

Accepted Answer

A)  $\$ 8000$ 
B)  $\$ 5000$ 
C)  $\$ 6000$ 
D)  $\$ 4000$ 
A)  $\$ 8000$ 
B)  $\$ 5000$ 
C)  $\$ 6000$ 
D)  $\$ 4000$

Question 12

Solve the system of equations by the elimination method.
-$$\begin{array} { l } 
2.5 x + 0.3 y = 10.6 \
0.5 x + 0.9 y = 3.8
\end{array}$$

Accepted Answer

A)  $( 6.5,2.3 )$ 
B)  $( 4,2 )$ 
C)  $( 4.5,2 )$ 
D)  $( 1.5,2.3 )$ 
A)  $( 6.5,2.3 )$ 
B)  $( 4,2 )$ 
C)  $( 4.5,2 )$ 
D)  $( 1.5,2.3 )$

Question 13

Solve graphically.
-$\begin{array}{c}
3 x+2 y=5 \
-6 x-4 y=5
\end{array}$

Accepted Answer

A)  $( 1.5 , - 1 )$ 
B)  No solution 
C)  $( 1,1 )$ 
D)  $( - 1.5 , - 1 )$ 
A)  $( 1.5 , - 1 )$ 
B)  No solution 
C)  $( 1,1 )$ 
D)  $( - 1.5 , - 1 )$

Question 14

Solve the problem using the elimination method.
-A salesman sold $\$ 200$ more than the rest of the sales staff. If the sales total for the day was $\$ 2050$, how much did the rest of the sales staff sell?

Accepted Answer

A)  $\$ 1125$ 
B)  $\$ 925$ 
C)  $\$ 1850$ 
D)  $\$ 1025$ 
A)  $\$ 1125$ 
B)  $\$ 925$ 
C)  $\$ 1850$ 
D)  $\$ 1025$

Question 15

Solve graphically.
-$\begin{array} { l } 
3 x + 4 y = 31 \
4 x - 2 y = 34
\end{array}$

Accepted Answer

A)  No solution 
B)  $( 1,9 )$ 
C)  $( 3,22 )$ 
D)  $( 9,1 )$ 
A)  No solution 
B)  $( 1,9 )$ 
C)  $( 3,22 )$ 
D)  $( 9,1 )$

Question 16

Solve.
-A cruise boat travels 48 miles downstream in 3 hours and returns to its starting point upstream in 12 hours. Find the speed of the stream.

Accepted Answer

A)  $16 \mathrm { mph }$ 
B)  $10 \mathrm { mph }$ 
C)  $6 \mathrm { mph }$ 
D)  $26 \mathrm { mph }$ 
A)  $16 \mathrm { mph }$ 
B)  $10 \mathrm { mph }$ 
C)  $6 \mathrm { mph }$ 
D)  $26 \mathrm { mph }$

Question 17

Solve graphically.
-$\begin{array}{c}
3 x-2 y=4 \
-6 x+4 y=7
\end{array}$

Accepted Answer

A)  Infinite number of solutions 
B)  $( 2,1 )$ 
C)  No solution 
D)  $( 1,2 )$ 
A)  Infinite number of solutions 
B)  $( 2,1 )$ 
C)  No solution 
D)  $( 1,2 )$

Question 18

Solve the problem using the elimination method.
-Two angles are supplementary, and one is $5 ^ { \circ }$ more than six times the other. Find the larger angle.

Accepted Answer

A)  $25 ^ { \circ }$ 
B)  $155 ^ { \circ }$ 
C)  $70 ^ { \circ }$ 
D)  $110 ^ { \circ }$ 
A)  $25 ^ { \circ }$ 
B)  $155 ^ { \circ }$ 
C)  $70 ^ { \circ }$ 
D)  $110 ^ { \circ }$

Question 19

Solve graphically.
-$\begin{array} { l } 
\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = 5 \
\frac { 5 } { 2 } x + \frac { 2 } { 3 } y = 12
\end{array}$

Accepted Answer

A)  $( 4 , - 3 )$ 
B)  $( 3,4 )$ 
C)  $( 4,3 )$ 
D)  $( 3,1 )$ 
A)  $( 4 , - 3 )$ 
B)  $( 3,4 )$ 
C)  $( 4,3 )$ 
D)  $( 3,1 )$

Question 20

Solve the problem.
-A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

Accepted Answer

A) 44 one-dollars 
B) 42 one-dollars 
C) 37 one-dollars 
D) 47 one-dollars 
A) 44 one-dollars 
B) 42 one-dollars 
C) 37 one-dollars 
D) 47 one-dollars

Classify the system as consistent or inconsistent, and dependent or independent. - 4x+4y=1 8x+8y=2

Solve the problem using the elimination method. -In a right triangle, one acute angle is $54 ^ { \circ }$ more than twice the other. Find each acute angle.

Solve by the substitution method. - 7x+9y=-54 -3x-4y=24

Solve by the substitution method. - 8x+8y=-32 5x-4y=-20

Solve. -A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5 mph slower than the power boat. Find the speed of each boat.

Solve the system of equations by the elimination method. - 3x-5y=2 18x-30y=12

Solve. -Jill is 27.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2.5 kilometers per hour. They meet in 5 hours. How fast is Joe walking?

Solve. -An express and local train leave GraysLake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Solve. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 7 miles per hour, and Delvis is traveling at the speed of 4 miles per hour. In 2 hours what is the distance between them?

Solve the problem using the elimination method. -Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 81$ for 3 days and 300 miles, while Mary was charged $\$ 145$ for 5 days and 600 miles. What does Best Rental charge per day and per mile?

Solve the problem. -Walt made an extra $\$ 10,000$ last year from a part-time job. He invested part of the money at $10 \%$ and the rest at $9 \%$ . He made a total of $\$ 960$ in interest. How much was invested at $9 \%$ ?

Solve the system of equations by the elimination method. - 2.5x+0.3y=10.6 0.5x+0.9y=3.8

Solve graphically. - 3x+2y=5 -6x-4y=5 $Solve graphically. - \begin{array}{c} 3 x+2 y=5 \\ -6 x-4 y=5 \end{array}$

Solve the problem using the elimination method. -A salesman sold $\$ 200$ more than the rest of the sales staff. If the sales total for the day was $\$ 2050$ , how much did the rest of the sales staff sell?

Solve graphically. - 3x+4y=31 4x-2y=34 $Solve graphically. - \begin{array} { l } 3 x + 4 y = 31 \\ 4 x - 2 y = 34 \end{array}$

Solve. -A cruise boat travels 48 miles downstream in 3 hours and returns to its starting point upstream in 12 hours. Find the speed of the stream.

Solve graphically. - 3x-2y=4 -6x+4y=7 $Solve graphically. - \begin{array}{c} 3 x-2 y=4 \\ -6 x+4 y=7 \end{array}$

Solve the problem using the elimination method. -Two angles are supplementary, and one is $5 ^ { \circ }$ more than six times the other. Find the larger angle.

Solve graphically. - x-y=5 x+y=12 $Solve graphically. - \begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = 5 \\ \frac { 5 } { 2 } x + \frac { 2 } { 3 } y = 12 \end{array}$

Solve the problem. -A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

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