Question 1

Solve by the substitution method.
-x + y = -6 x + y = -4

Accepted Answer

A) No solution 
B) (0, 0) 
C) (-6, -4) 
D) (0, -10) 
A) No solution 
B) (0, 0) 
C) (-6, -4) 
D) (0, -10)

Question 2

Solve the problem.
-The perimeter of a rectangle is 50 m. If the width were doubled and the length were increased by 5 m, the perimeter would be 74 m. What are the length and width of the rectangle?

Accepted Answer

A) width 7 m, length 12 m 
B) width 12 m, length 12 m 
C) width 7 m, length 18 m 
D) width 18 m, length 7 m 
A) width 7 m, length 12 m 
B) width 12 m, length 12 m 
C) width 7 m, length 18 m 
D) width 18 m, length 7 m

Question 3

Match the inequality with a graph.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

Solve.
-A $136,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 9%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $10,560 annual income from the
Investments, how much should the bank invest in bonds?

Accepted Answer

A) $68,000 
B) $50,000 
C) $16,000 
D) $18,000 
A) $68,000 
B) $50,000 
C) $16,000 
D) $18,000

Question 5

Solve graphically.
-

Accepted Answer

A) (2, 15) 
B) No solution 
C) (8, 9) 
D) (9, 8) 
A) (2, 15) 
B) No solution 
C) (8, 9) 
D) (9, 8)

Question 6

Solve.
-The speed of a stream is 4 mph. If a boat travels 60 miles downstream in the same time that it takes to travel 30 miles upstream, what is the speed of the boat in still water?

Accepted Answer

A) 12 mph 
B) 15 mph 
C) 14 mph 
D) 8 mph 
A) 12 mph 
B) 15 mph 
C) 14 mph 
D) 8 mph

Question 7

Solve.
-Mike, Joe, and Bill are painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours or if Mike and Joe work together for 2 hours and Bill works alone for 5 hours,
Or if Mike works alone for 6 hours, Joe works alone for 2 hours, and Bill works alone for 1 hour. How much time
Does it take for each man working alone to complete the painting?

Accepted Answer

A) Mike 12 hr, Joe 10 hr, Bill 10 hr 
B) Mike 8 hr, Joe 16 hr, Bill 8 hr 
C) Mike 16 hr, Joe 8 hr, Bill 8 hr 
D) Mike 8 hr, Joe 8 hr, Bill 16 hr 
A) Mike 12 hr, Joe 10 hr, Bill 10 hr 
B) Mike 8 hr, Joe 16 hr, Bill 8 hr 
C) Mike 16 hr, Joe 8 hr, Bill 8 hr 
D) Mike 8 hr, Joe 8 hr, Bill 16 hr

Question 8

Choose the ordered pair which is a solution of the inequality.
-

Accepted Answer

A) (1, 1) 
B) (3, 2) 
C) (2, 2) 
D)    
A) (1, 1) 
B) (3, 2) 
C) (2, 2) 
D)

Question 9

Solve.
-From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 7 miles per hour. In how many hours will they be 80 miles apart?

Accepted Answer

A) 6 hours 
B) 1 hour 
C) 7 hours 
D) 5 hours 
A) 6 hours 
B) 1 hour 
C) 7 hours 
D) 5 hours

Question 10

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

Accepted Answer

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

Question 11

Classify the system as consistent or inconsistent, and dependent or independent.
-x + y = -12 2x - 2y = -12

Accepted Answer

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

Question 12

Solve the problem using the elimination method.
-In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

Accepted Answer

A) 28° and 62° 
B) 37° and 53° 
C) 21° and 69° 
D) 12° and 78° 
A) 28° and 62° 
B) 37° and 53° 
C) 21° and 69° 
D) 12° and 78°

Question 13

Solve the problem using the elimination method.
-The sum of two numbers is 104. The second number is three times as large as the first number. What are the numbers?

Accepted Answer

A) 26 and 78 
B) 23 and 81 
C) 24 and 72 
D) 24 and 80 
A) 26 and 78 
B) 23 and 81 
C) 24 and 72 
D) 24 and 80

Question 14

Solve the problem.
-Anne and Nancy use a metal alloy that is 17% copper to make jewelry. How many ounces of an alloy that is 11% copper must be mixed with an alloy that is 22% copper to form 55 ounces of the desired alloy?

Accepted Answer

A) 25 ounces 
B) 30 ounces 
C) 35 ounces 
D) 27 ounces 
A) 25 ounces 
B) 30 ounces 
C) 35 ounces 
D) 27 ounces

Question 15

Solve.
-x + y = 2 4y + 4z = 16
3x + z = 6

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

Solve.
-7x + 7y + z = 1 x + 8y + 8z = 8
9x + y + 9z = 9

Accepted Answer

A) (1, -1, 1) 
B) (-1, 1, 1) 
C) (0, 1, 0) 
D) (0, 0, 1) 
A) (1, -1, 1) 
B) (-1, 1, 1) 
C) (0, 1, 0) 
D) (0, 0, 1)

Question 17

Solve graphically.
-

Accepted Answer

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

Question 18

Solve the problem using the elimination method.
-A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 5 bags of potato chips for $9.50. Another customer buys 2 hot dogs and 5 bags of potato chips for $8.00. Find the cost of each item.

Accepted Answer

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

Question 19

Solve the problem.
-Find two numbers whose sum is 42 and whose difference is 0.

Accepted Answer

A) 23 and 23 
B) 21 and 21 
C) 43 and -1 
D) 19 and 23 
A) 23 and 23 
B) 21 and 21 
C) 43 and -1 
D) 19 and 23

Question 20

Solve.
-x + y + z = 7 x - y + 2z = 7
5x + y + z = 11

Accepted Answer

A) (1, 4, 2) 
B) (1, 2, 4) 
C) (4, 1, 2) 
D) (4, 2, 1) 
A) (1, 4, 2) 
B) (1, 2, 4) 
C) (4, 1, 2) 
D) (4, 2, 1)

Solve by the substitution method. -x + y = -6 x + y = -4

Solve the problem. -The perimeter of a rectangle is 50 m. If the width were doubled and the length were increased by 5 m, the perimeter would be 74 m. What are the length and width of the rectangle?

Match the inequality with a graph. -

Solve. -A $136,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 9%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $10,560 annual income from the Investments, how much should the bank invest in bonds?

Solve graphically. -

Solve. -The speed of a stream is 4 mph. If a boat travels 60 miles downstream in the same time that it takes to travel 30 miles upstream, what is the speed of the boat in still water?

Choose the ordered pair which is a solution of the inequality. -

Solve. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 7 miles per hour. In how many hours will they be 80 miles apart?

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

Classify the system as consistent or inconsistent, and dependent or independent. -x + y = -12 2x - 2y = -12

Solve the problem using the elimination method. -In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

Solve the problem using the elimination method. -The sum of two numbers is 104. The second number is three times as large as the first number. What are the numbers?

Solve the problem. -Anne and Nancy use a metal alloy that is 17% copper to make jewelry. How many ounces of an alloy that is 11% copper must be mixed with an alloy that is 22% copper to form 55 ounces of the desired alloy?

Solve. -x + y = 2 4y + 4z = 16 3x + z = 6

Solve. -7x + 7y + z = 1 x + 8y + 8z = 8 9x + y + 9z = 9

Solve graphically. -

Solve the problem using the elimination method. -A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 5 bags of potato chips for $9.50. Another customer buys 2 hot dogs and 5 bags of potato chips for $8.00. Find the cost of each item.

Solve the problem. -Find two numbers whose sum is 42 and whose difference is 0.

Solve. -x + y + z = 7 x - y + 2z = 7 5x + y + z = 11

Solving Linear Equations and Inequalities

Graphs, Functions, and Applications

Polynomials and Polynomial Functions

Rational Expressions, Equations, and Functions

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Conic Sections

Filters

Exam 3: Systems of Equations

Solve by the substitution method. -x + y = -6 x + y = -4

Solve the problem. -The perimeter of a rectangle is 50 m. If the width were doubled and the length were increased by 5 m, the perimeter would be 74 m. What are the length and width of the rectangle?

Match the inequality with a graph. -

Solve. -A $136,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 9%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $10,560 annual income from the Investments, how much should the bank invest in bonds?

Solve graphically. -

Solve. -The speed of a stream is 4 mph. If a boat travels 60 miles downstream in the same time that it takes to travel 30 miles upstream, what is the speed of the boat in still water?

Choose the ordered pair which is a solution of the inequality. -

Solve. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 7 miles per hour. In how many hours will they be 80 miles apart?

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

Classify the system as consistent or inconsistent, and dependent or independent. -x + y = -12 2x - 2y = -12

Solve the problem using the elimination method. -In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

Solve the problem using the elimination method. -The sum of two numbers is 104. The second number is three times as large as the first number. What are the numbers?

Solve the problem. -Anne and Nancy use a metal alloy that is 17% copper to make jewelry. How many ounces of an alloy that is 11% copper must be mixed with an alloy that is 22% copper to form 55 ounces of the desired alloy?

Solve. -x + y = 2 4y + 4z = 16 3x + z = 6

Solve. -7x + 7y + z = 1 x + 8y + 8z = 8 9x + y + 9z = 9

Solve graphically. -

Solve the problem using the elimination method. -A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 5 bags of potato chips for $9.50. Another customer buys 2 hot dogs and 5 bags of potato chips for $8.00. Find the cost of each item.

Solve the problem. -Find two numbers whose sum is 42 and whose difference is 0.

Solve. -x + y + z = 7 x - y + 2z = 7 5x + y + z = 11

Solving Linear Equations and Inequalities

Graphs, Functions, and Applications

Polynomials and Polynomial Functions

Rational Expressions, Equations, and Functions

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Conic Sections

Filters