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  2 x  2
Solve the following systems of linear equations using the Substitution Method (circle your final
answer):
Check your answer:
4x  7y  2
3.)
x  y  5
4.)
4x  y  10
2x  4y  16
Solve the following systems of linear equations using theElimination Method (circle your final
answer):
5.)
6.)
3x  2y  12
7x  2y  8
9x  3y  24
11x  2y  1
Check your answer:
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.)
4x  5 y  11
6x  7 y  31
Select the correct answer that lists the solution to the system.
A.
8.)
3

 , 1
2
B.
1, 4 
C.
4,1
D. The system has no solution
y x4
x  3y  12
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.)
2 x  3y  2
4 x  6 y  7
This system of linear equations has _______________ solutions, the system is
________________________________________________________
10.)
6x  10y  30
3x  5y  15
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  2x  2
Chapter 6 - Systems of Linear Equations & Inequalities Sample Test 5
13.) Solve the following system of inequalities by graphing. LABEL THE FEASIBLE REGION!
2x  y  3
2x - y  -1
14.) Choose the answer that defines the system of linear inequalities shown in the graph below:
A.
y  2x  1
y  x  2
B.
y  2x  1
y  x  2
C.
y  2x  1
y  x  2
D.
y  2x  1
y  x  2
15.) The sum of two numbers is 20. The larger number is 5 more than the smaller number. What are
the two numbers? _________________________________________
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?