Name ______________________________
Class __________ Date __________
Algebra 2 – Chapter 3 Study Guide
Directions: Show all work and reasoning to receive full credit.
1) Classify the system without graphing.
What does this mean in terms of the number of solutions to the system?________________
 x  2 y  13

2 y  7  x
Solve each system using the given method.
2) Graphing
 x  2 y  6

4 x  y  4
3) Substitution
4) Elimination
2 x  y  7

3x  2 y  10
4 x  3 y  6

5 x  6 y  27
1
1
5) Suppose the drama club is planning a production that will cost $525 for the set and $150 per performance. A sold-out
performance will bring in $325. Write an equation for the cost C and an equation for the income I for p sold-out performances.
How many sold-out performances will it take for the club to break even?
6)
Suppose you are buying two kinds of notebooks for school. A spiral notebook costs $2, and a three-ring notebook costs $5. You
must have at least six notebooks. The cost of the notebooks can be no more than $20.
a.
Write a system of inequalities to model the situation.
Let x be the number of spiral notebooks and y be the number of 3-ring notebooks.
b.
Graph and solve the system.
Name ______________________________
Class __________ Date __________
Solve each system of inequalities by graphing.
7)
3  2 x  y

x  3y  4
8)
  x  2 y  6

 y  2 x  3  4
8
8
6
6
4
4
2
2
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
-8 -7 -6 -5 -4 -3 -2 -1
-2
-2
-4
-4
-6
-6
-8
-8
1 2 3 4 5 6 7 8
Graph each system of constraints. Find all vertices. Evaluate the objective function at each vertex to find the maximum and
minimum value.
9)
x  2 y  6

x  2
y 1

Minimum for C = 3x +4y
10)
x  y  6

2 x  y  10
 x  0, y  0

Maximum for P = 4x + y
Vertices: _______________________________________
Vertices: ____________________________________
Minimum: __________________
Maximum: _________________
Name ______________________________
Class __________ Date __________
11a)
Suppose you make and sell lotion. A quart of regular skin lotion contains 2 c. oil and 1 c. cocoa butter. A quart of extra-rich
lotion contains 1 c. oil and 2 c. cocoa butter. You will make a profit of $10/qt on regular lotion and a profit of $8/qt on extrarich lotion. You have 24 c. oil and 18 c. butter. Write and graph a system of inequalities to model the situation and graph; let
x be the number of quarts of regular lotion, and let y be the number of quarts of extra-rich lotion. How many quarts of each
type of lotion should you make to maximize your profit? ***Hint: To accurately find your vertices, solve a system of
equations to find the intersection of your two boundaries.
11b)
What is the maximum profit?
Solve the system of equations.
12)
 2 x  3 y  z  3

x  5 y  7 z  11

10 x  4 y  6 z  28

Write a system of equations and solve.
13)
The sum of three numbers is -2. The sum of three times the first number, twice the second number, and the third number is 9.
The difference between the second number and half the third number is 10. Find the numbers.