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Name ______________________________________
Block ___________________
Systems Unit Test Review
Graph each system of equations and state its solution. Then state whether the
system is consistent and independent, consistent and dependent, or inconsistent.
1)
x 1  y
2)
2x  2 y  8
3
x y 0
4
3)
y x
 6
3 2
x y 4
5) 2 x  3 y  9
4)
x  2y  5
3 x  15  6 y
x  y 1
3x  5 y  7
Name ______________________________________
Block ___________________
Write a system of equations for each problem and solve by graphing.
6) George bought 7 quarts of cleaning fluid: x quarts at $3.00 per quart and y quarts at
$2.00 per quart. Find x and y if the total cost was $16.00.
Solve each system of equations by the substitution method.
(Need to do on notebook paper)
y  3x
6 x  4 y  6
7)
8)
x  2 y  21
3x  y  3
9)
3 x  4 y  7
2x  2 y  4
10)
x  2y  0
x
7
4
 y
3
3
Solve each system of equations by the elimination method.
11)
13)
4x  y  9
12)
3x  2 y  4
4 x  3 y  4
14)
4 x  3 y  4
2x  y  0
5x  3 y  1
8x  3 y  4
4 x  9 y  5
Solve each system of equations.
15)
3 x  6 y  42
 x  2 y  14
16)
3y  2x  4
17) 1
3 y  4x   1
6
18)
2x  3y  8
x y 2
2 y  4x  0
2 x  y  2  0
Name ______________________________________
Block ___________________
Solve the Problem.
19) The sum of two numbers is 42. Their difference is 12. What are the two numbers?
20) A painter has exactly 32 units of yellow dye and 54 units of green dye. He plans to
mix as many gallons as possible of color A and color B. Each gallon of color A requires 4
units of yellow dye and 1 unit of green dye. Each gallon of color B requires 1 unit of
yellow dye and 6 units of green dye.
a) Let x be the number of gallons of color A and let y be the number of gallons of
color B. Write the inequalities.
b) Graph the system of inequalities and name the vertices of the polygon formed.
c) Find the maximum number of gallons, x + y, possible.
21) A farmer has 20 days in which to plant corn and beans. The corn can be planted at a
rate of 10 acres per day and the beans at a rate of 15 acres per day. The farm has 250
acres available.
a) Let x be the number of acres of corn and let y be the number of acres of beans.
Write the inequalities that represent the situation.
b) Graph the system of inequalities and name the vertices of the polygon formed.
c) If corn profits $30 per acre and beans profit $25 per acre, find the values of x and
y to maximize the profit.
d) If corn profits $29 per acre and beans profits $30 per acre, find the values of x and
y to maximize the profit.
22) A dressmaking shop makes dresses and pantsuits. The equipment in the shop allows
for making at most 30 dresses and 20 pantsuits in a week. It takes 10 worker hours to
make a dress and 20 worker hours to make a pantsuit. There are 500 worker hours in a
week in the shop.
a) If the profit on a dress and the profit on a pantsuit are the same, how many of each
should be made to maximize the profit?
b) If the profit on a pantsuit is three times the profit on a dress, how many of each
should be made to maximize the profit?
Solve each System
a  2b  c  9
23) 2b  3c  16
4b  8
4x  2 y  5z  6
26) 3 x  3 y  8 z  4
x  5 y  3z  5
x  y  z  1
24) 2 x  y  2
3x  9
x  y  5 z  2
27) 3 y  6 z  6
2x  4 y  2z  8
2 x  4 y  z  3
25) y  z  4
2 y  2
Name ______________________________________
Block ___________________
Solve the system of inequalities by graphing.
28)
30)
32)
y5
x  1
x y 3
2x  3 y  6
x2 3 y
x  y 1
29)
31)
y  2x  2
y  x  2
x 5  y
x y 6
y2
33) y  2 x
y  x 1
Name ______________________________________
Block ___________________
Answers
1) no solutions, inconsistent
2) ( x, y) | x  2 y  5 consistent and dependent
3) (8,6); consistent and independent
4) (-1,2); consistent and independent
5) (3,1); consistent and independent
x2
6)
y5
7) (-3, -9)
10)
8)
 13 , 2
9)
 x, y  |3x  4 y  7
13) No Solution
 14 4 
16)  , 
 5 5
 43 , 23 
11) (2,1)
 1 2
14) 

 4, 3 
2

17)  1, 
3

15)
12) (-1,2)
 x, y  |3x  6 y  42
18) No Solution
20) a) x  0, y  0, 4 x  y  32, x  6 y  54
b)  0,9 , 8,0 ,  0,0  ,  6,8
c) 14 gallons  6 A,8B 
x
y
  20
10 15
b) 100,150 ,  200,0 ,  0,0 ,  0, 250 
c) 100 acres of corn, 150 acres of beans
d) 0 acres of corn, 250 acres of beans
21) a) x  0, y  0, x  y  250,
22) 18. a) 30 dresses, 10 pantsuits
b) 10 dresses, 20 pantsuits
23)
 9, 2, 4
24.
 3, 4,0
25.
 3, 1,5
26. No Solution 27. Infinitely Many Solutions
28)
29)
Solution
Solution
19) 27,15
Name ______________________________________
30)
Solution
Block ___________________
31)
Solution
Solution
32)
33)
Solution