Chapter 6 - Systems of Linear Equations & Inequalities Sample Test 1

Name: _____________________________________

SHOW ALL WORK! No work, no credit

1.) Solve the following systems of equations graphically. The solution is ___________

y=x+3 y=− x−5

2.) Solve the following system of equations graphically. The solution is ______________

x− y=4 y=−2x+2

Solve the following systems of linear equations using the Substitution Method (circle your final answer):

3.)

4.)

Solve the following systems of linear equations using theElimination Method (circle your final answer):

5.)

6.)

Check your answer:

Check your answer:

9x 3y 24

11x 2y 1

Chapter 6 - Systems of Linear Equations & Inequalities Sample Test 3

Solve the following systems of linear equations (#7 & 8) using either substitution or elimination (circle your solution). Question 7 is a multiple choice question and in question #8 explain why you chose the method you did.

7.)

4 x−5 y=116 x+7 y=31

Select the correct answer that lists the solution to the system.

A. B. C. D. The system has no solution

8.)

I chose the _____________________________________ method because

________________________________________________________________________________________________

For the following systems of linear equations (#9 & 10) solve using the method of your choice and determine if the system has 1 solution, no solutions, or infinite solutions. Then determine if the system is consistent and independent, consistent and dependent, or inconsistent.

9.)

This system of linear equations has _______________ solutions, the system is ________________________________________________________

y x 4

x 3y 12

2x 3y 2

4x 6y 7

10.)

This system of linear equations has _______________ solutions, the system is __________________________________________________________________

11.) Graph the linear inequality: y <x – 4

12.) Solve the following system of inequalities by graphing. LABEL THE FEASIBLE REGION!

y≥−3 x+2 y<2 x+2

6x 10y 30

3x 5y 15

Chapter 6 - Systems of Linear Equations & Inequalities Sample Test 5

13.) Solve the following system of inequalities by graphing. LABEL THE FEASIBLE REGION!

2 x+ y<−3 2x-y≤-1

14.) Choose the answer that defines the system of linear inequalities shown in the graph below:

15.) The sum of two numbers is 20. The larger number is 5 more than the smaller number. What are the two numbers? _________________________________________

A.

B.

C.

D.

16.) You are in Chemistry lab and in order to pass your lab you need to mix two acid solutions together. One solution is 8% acid and another solution is 18% acid. How many gallons of each acid should be mixed together to produce 30 gallons of a solution that is 12% acid?

Let x = the liters of 8% sodium solution let y = the liters of 18% sodium solution

Write an equation for total volume of solution:

Write an equation for total volume of acid:

17. A carpenter makes and sells rocking chairs. The material for each chair costs $25. The chairs sell for $125 each. If the carpenter spends $3000 start up costs, how many chairs must he sell to break even? Let x = the number of chairs made and sold Let y = the dollars of expense or income

Expense = _______________________________________ Income = _________________________________________

Break-even is where expenses = income, use this relationship to solve the system of equations.

18. Bonus Problem: A dog walker earns $12 per hour. She also earns $18 per hour for babysitting. She wants to earn at least $360 next week, but can work no more than 30 hours. What is a graph showing how many hours she can work at each job?