Please Write on the Challenge

Unit 4 ChallengeForm_Preview_

Please write on the challenge.

Show All Work.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the given ordered pair is a solution to the system.

1) ( 8, 7)

6x - 5y = 13

9y =3x + 40

A) YesB) No

Solve by the method of your choice. Identify whether the system has no solution or infinitely many solutions, using set notation to express the solution set.

2) 2x + y = 6

y = 8 - 2x

A) {(5,-4)}B)∅C) {(0, 6)}D) {(x, y) |2x + y = 6}

Let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers.

3) Two numbers total 14, and their difference is 20. Find the two numbers.

A) 7 and - 13B) 17 and - 3C) 14 and 2D) 8 and 6

Solve the problem.

4) Devon purchased tickets to the Blue Angels air show for 8 adults and 2 children. The total cost was $232. The cost of a child's ticket was $4 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

A) adult's ticket: $ 26; child's ticket: $ 22B) adult's ticket: $ 23; child's ticket: $ 19

C) adult's ticket: $ 24; child's ticket: $ 20D) adult's ticket: $ 25; child's ticket: $ 21

Solve the system by the addition method. Be sure to check all proposed solutions.

5) x - 2y = 2

-7x - 2y = 34

A) {( 3, -4)}B) {( -3, -4)}C) {( -4, -3)}D) ∅

Solve the system by the substitution method. Be sure to check all proposed solutions.

6) x + 2y = 40

y = 3x + 6

A) {( 4, 18)}B) {(-4, -6)}C) {( 5, 21)}D) {( 3, 15)}

Use the two steps for solving a linear programming problem to solve the problem.

7) Bruce is bringing items to sell at a flea market, where he plans to sell televisions at $125 each and DVD players at $100 each. Due to space limitations he can only store at most 150 items for the day. However, because more people already own televisions, Bruce knows that the number of DVD sales must at least match the number of television sales. How many of each item should Bruce bring to the flea market to maximize his sales?

A) 50 televisions and 100 DVD playersB) 25 televisions and 125 DVD

C) 100 televisions and 50 DVDD) 75 televisions and 75 DVD players

Solve the problem.

8) Benjamin never has more than 23 hours free during the week. He is trying to make a weekly plan for dividing his free time between reading and working out. He wants to spend at least 7 hours per week reading. Write a system of inequalities to describe the situation. Let x = amount of time for reading and y = amount of time for working out.

A) x + y ≤ 23

x ≥ 7

y ≥ 0

B) x + y ≤ 23

y ≥ 7

x ≥ 0

C) x + y ≤ 23

x ≥ 7y

x ≥ 0y ≥ 0

D) x + y ≤ 23

x ≤ 7y

x ≥ 0y ≥ 0

Graph the system of inequalities.

9) y ≥ 2x + 4

x + y ≤ -3

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Show all work.

Solve the system by graphing. Check the coordinates of the intersection point in both equations.

10) y = x + 5

y =-x + 7