Chapter 3 Test
Sections 1 – 4
Name _______________________________
Per. # ___________ Form A
1. Without Graphing Classify the equations as Independent, Dependent, or Inconsistent and explain why.
2
y  3  x  4
5
2 x  5 y  7
1. Independent, Dependent, or Inconsistent
1. Why? ___________________________
_________________________________________
_______________________________________(+3)
#2 & 3. Solve the system of equations by Graphing.
2
3
x  4
2. y  x  4
3. y  2 
3
4
x  y 1
2 x  y  10
Solution
is
2. ________(+6)
Solution
is
3. __________(+6)
#4 & 5. Solve the system of equations by Substitution. Show work for credit.
4. y  2 x  3
5. 3 x  4 y  10
3 x  2 y  10
2 x  6 y  24
Solution
is
Solution
is
4. ________________(+6)
5. ________________(+8)
#6 – 8. Solve the system of equations by Elimination. Show work for credit.
6. 4 x  2 y  56
7. 3 x  5 y  22
3 x  2 y  28
6 x  2 y  20
Solution
is
Solution
is
6. ________________(+6)
7. ________________(+7)
8. 2 x  3 y  1
5 x  4 y  37
Solution
is
8. ________________(+8)
9. Solve the System of Inequalities by graphing
3
y  x2
(+7)
4
2
y
x7
3
#10 & 11. Solve each System of Inequalities by graphing.
3
10. y  1   x  4 
(+9)
11. x  2 y  2
2
1
y
x3 2
y  3 x  2  1
2
(+9)
12. Find the values of x and y that Maximize the objective function for the graph. What is the maximum
value? Show your work.
(+5)
Maximum for P = 5x + 6y
13. Graph the system of constraints. Name all vertices. Then find the value of x and y that will Maximize the
objective function.
(+10)
x0
3 y 6
x y8
6 y  3 x  12
Maximum for P = 3x + 4y.
14. A business makes Fossil Ridge hats in green and black. The business can only produce at most 200
hats per day. Hat materials cost $3 per green hat and $5 per black hat. The business budgets $750 per
day for material expenses. Each green hat sells for $14 and each black hat sells for $16.
(+10)
(a) Write a system of linear inequalities to represent the business constraints.
(b) Graph the feasible region.
(c) Find all vertices, determine the income function, and tabulate the income possible at each point.
Vertex (x, y)
Income
(d) How much of each kind of hat should the business produce in order to maximize daily income?