CP Algebra II 10/19/15
Chapter 3 Review
ì2x + 3y = 4
1. Solve the system í
by SUBSTITUTION.
î x + 2y = 3
ì4 x - y = 12
2. Solve the system í
by ELIMINATION.
î3x + 2y = 31
ì y = 2x +1
3. Solve the system í
by GRAPHING.
î 4 x - 2y = 12
Name: ______________________________
4. Compute the following operations if...
é
ù
é
ù
é
ù
é
ù
A = ê 2 -5 ú B = ê 3 -1 ú C = ê 2 0 8 ú D = ê 6 10 ú
ë -7 1 û
ë 5 2 û
ë 9 -2 10 û
ë -7 1 û
a. A + B
b. A× B
c.
A + C× D
d. B -1
e.
A× B + 2D
é
ù
5. Find the inverse of ê 12 5 ú and verify that they inverses.
ë 2 1 û
ì3x - y = 13
6. Solve the system í
using MATRICES.
î6x + 5y = -23
ì y £ 2x - 3
7. Solve the system of inequalities by GRAPHING: í
î x + y ³ +6
8. Find a system of inequalities that would produce the feasible region.
9. Solve the system by ELIMINATION.
ì-2x + 3y - z = -25
ï
í3x - 7 y + 2z = 54
ï4x + 8y - 5z = -76
î
10. Mrs. Long is planning on taking her nephews on a backpacking trip! She will meet everyone’s daily
nutritional requirements with food bars and drink cartons. Each food bar contains 42 grams of
carbohydrates, 5 grams of fat and 6 grams of protein. Each drink carton contains 28 grams of
carbohydrates, 15 grams of fat and 12 grams of protein. Each backpacker will need at least 168
grams of carbohydrates, 45 grams of fat and 48 grams of protein.
a. Let x= # of food bars and y= # of drink cartons.
Write and graph the constraint inequalities.
CARBOHYDRATES:
PROTEIN:
FAT:
b. Use SUBSTITUTION to find the coordinates of the intersection of the CARBOHYDRATES and
PROTEIN boundary lines.
c.
Use INVERSE MATRICES to find the coordinates of the intersection of the PROTEIN and FAT
boundary lines.
d. Mrs. Long’s nephews are pretty young so she is trying to limit the total weight of the food.
Each food bar weighs 5 ounces and each drink carton weighs 7 ounces. How many food
bars and drink cartons should each camper pack per day to minimize the weight?