Algebra 3-4 Honors
Chapter 3 Test Review
𝑥+𝑦 =5
1. Solve the system by graphing. {
2𝑦 = 𝑥 − 2
Solution __________________________
Name ___________________________ Per ________
2𝑥 − 5𝑦 = 20
2. Solve the system by graphing. {
2𝑥 + 𝑦 = 8
Solution __________________________
Find the slope and y-intercept for each line in the system. Then use this information to determine if the system is
independent, dependent or inconsistent
3. {
3𝑥 − 4𝑦 = 5
6𝑥 − 8𝑦 = −5
2. m= _______ b=_______ m= _______ b=_______
Independent, dependent or inconsistent? _______________
4. {
2𝑥 − 7𝑦 = 14
𝑥 + 3𝑦 = 6
3. m= _______ b=_______ m= _______ b=_______
Independent, dependent or inconsistent? _______________
Solve using the substitution method.
5. {
𝑥 − 4𝑦 = 4
2𝑥 + 12𝑦 = 16
6. {
2𝑥 − 𝑦 = −4
4𝑥 + 𝑦 = 1
5. ______________________
6. ______________________
Solve using the elimination method.
7. {
5𝑥 + 2𝑦 = −8
4𝑥 + 3𝑦 = 2
8. {
2𝑥 − 𝑦 = 0
−3𝑥 + 𝑦 = 5
7. ______________________
8. ______________________
Graph the system of inequalities.
𝑥 − 2𝑦 < 6
9. {
2𝑥 + 𝑦 ≥ 8
𝑦 ≤𝑥+3
10. {
𝑦 > |𝑥 − 1|
Graph the constraints. Name the coordinates of the feasible region.
𝑥+𝑦 ≤5
𝑥 + 2𝑦 ≤ 8
11. {
0≤𝑥≤3
𝑦≥0
𝑥+𝑦 ≤5
12. { 4𝑥 + 𝑦 ≤ 8
𝑥 ≥ 0, 𝑦 ≥ 0
The vertices of the feasible region are (2,2) , (2,1) , and (4,1).
13. Find the value of x and y that maximizes the objective function C=3x+4y
13. ___________________
14. Find the value of x and y that minimizes the objective function P=x+3y
14. ___________________
Solve using the substitution method.
𝑥 − 2𝑦 = 1
15. {𝑥 + 3𝑦 + 𝑧 = 0
2𝑥 − 2𝑧 = 18
_________________
𝑥 + 𝑦 + 4𝑧 = 6
16. { −2𝑥 + 2𝑧 = 6
3𝑥 + 𝑦 − 2𝑧 = 0
_________________
𝑥−𝑦−𝑧 =0
18. { 𝑥 − 2𝑦 − 2𝑧 = 3
−2𝑥 + 2𝑦 − 𝑧 = 3
_________________
Solve using the elimination method.
2𝑥 − 𝑦 + 𝑧 = −4
17. { 3𝑥 + 𝑦 − 2𝑧 = 0
3𝑥 − 𝑦 = −4
_________________
Solve using any method.
 5 x  3 y  4 z  2

19.  3x  y  z  4
 x  6 y  5 z  4

 x yz 4

20.  2 x  y  z  5
 x  y  2 z  13

Define your variables. Write a system of equations. Use it to solve the problem.
21. A large can of tomatoes sells for $0.82 and a small can for $0.56. Ted buys several cans for a total of $3.58. If he
spent $1.34 more for the large cans than for the small cans, how many cans of each size did he buy?
22. A certain recipe calls for 5 cups of sugar and flour together. If the recipe had called for ¼ cup more sugar, there
would be twice as much flour as sugar. How much sugar does the recipe call for?
23. The average of two numbers is 11/24. One third of their difference is 1/12. Find the two numbers.
24. Five times one number is 3 less than twice another number. If the sum of the numbers is 26, find the numbers.
25. A collection of dimes and quarters has a total value of five dollars and contains 29 coins. How many of each coin is
in the collection.
26. The first number is three more than twice the second number. Half the sum of the numbers is five. Find the
numbers.
27. Frank needs to apply a 10% liquid nitrogen solution to his rose garden, but he has only a 4% liquid nitrogen solution
and a 20% liquid nitrogen solution available. How much of the 4% solution and the 20% solution should Frank mix
together to get 10 gallons of the 10% solution.
Review Answers:
13. (4,1)
22. x=cups flour, y=cups sugar ;
1. (4,1)
14. ( 2,1)
 x y5
; (3.5,1.5)

 x  2( y  0.25)
2. (5.-2)
15. (3,1,-6)
23. x=1st number, y=2nd number ;
3. 3/4 ; -5/4 ; 3/4 ; 5/8 ;
inconsistent
16. (-3,9,0)
19. (2,-4,6)
24. x=1st number, y=2nd number ;
20. (5,2,-3)
5 x  2 y  3
; (7,19)

 x  y  26
17. (-1,1,-1)
4. 2/7 ; -2 ; -1/3 ; 2 ; independent
5. (28/5, 2/5)
6. (-1/2, 3)
7. (-4/6)
21. x=#large, y=#small ;
0.82 x  0.56 y  3.58
; (3,2)

0.82 x  0.56 y  1.34
8. (-5,-10)
9.
18. (-3,-3,-1)
11
1
 2 ( x  y )  24
; (7/12,1/3)
1
1
 ( x  y) 
12
3
Shaded
area
25. x=# dimes, y=#quarters ;
x  y  29

; (15,14)

0.10 x  0.25 y  5.00
26. x=1st number, y=2nd number ;
 x  2 y  3
 1 ( x  y )  5 ; (23/3,7/3)
 2
10.
Shaded
area
27. x=#gallons 4%, y=#gallons 20%
x  y  10

;
0.04 x  0.20 y  0.10(10)
;
(6.25,3.75)
11.
Shaded
area
12.
Shaded
area