Semester Exam Review: Chapter 3
Solve each system equations by graphing.
 y  3x  2
x  2y  6
 4x  3y  6
2x  3y  12
1. 
2. 
Solve each system equations using substitution:
6x  2y  2
 y  2x  3
2x  4y  6
x  y  3
3. 
4. 
Solve each system of equations using elimination.
5x  7y  2
3x  4y
4x  6y  26
2x  3y  13
5. 
6. 
Set up a system for each of the following then solve.
7. A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager
decides to sell a 20-pound bag mixture for $47.50. How many pounds of each will be in the
mixture?
8. A Broadway theater has 500 seats left to sell divided into orchestra and balcony seats.
Orchestra seats sell for $50, and balcony seats sell for $25. If they sell all the seats their sell
will total revenue will be $18,000. How many of each ticket will they have to sell?
Given the following system of equations, find the value of x, y, and z.
2x  y  5
9.
3y  z  0
x  4z  14
xyz 1
10.
2x  3y  z  3
x  2y  4z  4
Graph each system of constraints. Find all vertices. Then find the Max/Min as indicated.
x  y  8

11.  y  5
x  0

Minimum for P = 3x + 2y
12. Set up a system of constraints and an objective function. DO NOT SOLVE.
A fish market buys tuna for $0.50 per pound and spends $1.50 per pound to clean and package it.
Salmon costs $2.00 per pound to buy and $2.00 per pound to clean and package. The market
makes $2.50 per pound profit on tuna and $2.80 per pound profit for salmon. The market can
spend only $106 per day to buy fish and $134 per day to clean it. How much of each type of fish
should the market buy to maximize profit?
Objective Function: ________________________________
Constraints:
13. Set up and solve.
Kay grows tomatoes and beans. It costs $1 to grow a bushel of tomatoes, and it costs $3 to grow a
bushel of beans. It takes 1 square yard of land to grow a bushel tomatoes and it takes 6 square yards
of land to grow a bushel of green beans. Kay’s budget is $15, and she has 24 square yards of land
available. If she makes $1 profit on each bushel of tomatoes and $4 profit on each bushel of beans,
how many bushels of each should she grow in order to maximize profits?
Objective Function ________________________
Constraints: