Algebra A
Name: _______________________
Unit 3: Linear Systems Practice Test ANSWERS
[Please see end of this FIRST!!!]
Solve each system using the GRAPHING method. (3 points each)
 x  3y  6
1) 
2 x  y  7
1

y  x  1
2) 
2
 x  y  3
(3, 1)
y
y
8
7
6
5
4
3
2
1
–8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
x
–8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
Solve each system using the SUBSTITUTION method.
 y x2
 y  3 x  10
3) 
y  x  2  (2)  2  4
(3 points each)
 y  x 5
3 x  2y  15
y  x  5  (5)  5  0
4) 
3 x  2 x  10  15
4 x  2  10
5 x  25
4x  8
x  5
x2
(2, 4)
(–5, 0)
Solve each system using the ELIMINATION method.
 3x  y  6
5 x  y  10
x
 y  x  5

3 x  2y  15
3 x  2( x  5)  15
 y  x  2

 y  3 x  10
x  2  3 x  10
5) 
1 2 3 4 5 6 7 8
3(2)  y  6
6y 6
(3 points each)
 9 x  3y  6
8 x  2y  4
6) 
y 0
 3x  y  6

5 x  y  10
9( 4)  3 y  6
36  3 y  6
3 y  42
y  14
 9 x  3 y  6 2  18 x  6 y  12

8 x  2y  4 3  24 x  6 y  12
6 x  24
8 x  16
x2
x  4
(2, 0)
(–4, –14)
7) To rent video equipment, Company A charges $60 plus $12 per hour. Company B
charges $80 plus $10 per hour.
a. Write a system of equations. State what x and y represent. (2 points)
Equation 1: y = 60 + 12x
x: number of hours
Equation 2: y = 80 + 10x
y: cost
b. Find the break-even point. Explain what it means in this problem. (2 points)
Break-even point: (10, 180)  you can use substitution, or simply make a table
Meaning:
the cost would be the same for each company to rent for 10
hours (the cost would be $180)
c. State which rental company should be used to keep costs to a minimum.
(1 points)
▪ Choose Company A if time will be LESS than 10 hours
▪ Choose Company B if time will be MORE than 10 hours
8) Riley spent $7.25 at a bakery for 3 bagels and 2 muffins. Karen bought 5 bagels and 4
muffins for $13.25. Find the cost of each item. (4 points)
Equation 1: 3x + 2y = 7.25
x: cost of bagels
Equation 2: 5x + 4y = 13.25
y: cost of muffins
3 x  2y  7.25   2  6 x  4 y  14.50

 5 x  4 y  13.25  5 x  4 y  13.25
1x  1.25
x  1.25
3(1.25)  2y  7.25
3.75  2y  7.25
2y  3.50
Bagel: $1.25 Muffin: $1.75
y  1.75
9) Buddy wants to start a business building and selling canoes. He will charge $500 for
each one. His building costs will be $190 per canoe. He must pay $9000 per month rent
(which includes utilities and equipment) so that he has a place to build and sell the canoe.
a. Write a rule for his revenue. (1 point)
R(x) = 500x
b. Write a rule for his costs. (1 point)
C(x) = 9000 + 190x
c. Write a rule for his profit. (1 point)
P(x) = 310x – 9000
d. What are his revenue, costs, and profit if he sells 5 canoes in one month? (1 point)
Revenue = $2500  500(5)
Costs = $9950  9000 + 190(5)
Profit = –$7450  310(5) – 9000
e. How many canoes will he have to sell in order to break even? (1 point)
Revenue = Cost  500 x  9000  190 x
310 x  9000
30 canoes
x  29.03
f. If Buddy wants to make a profit of $2000 each month, how many canoes will he
have to sell? (1 point)
2000  310 x  9000
11000  310 x
36 canoes
x  35.48
Solve each system using the method of your choice. You must clearly show what you do.
The graphs are there ONLY if you decide to use the graphing method. (3 points each)
5 x  2y  48
2 x  3 y  23
 x  y  12
3 x  3 y  36
11) 
10) 
 x  y  12   3 3 x  3 y  36

 3 x  3y  36  3 x  3 y  36
00
2( 10)  3 y  23
20  3 y  23
3 y  3
y  1
5 x  2y  48 3  15 x  6y  144

 2x  3y  23 2  4 x  6y  46
19 x  190
x  10
Infinite solutions
(–10, –1)
Review
Given the table, tell whether the table is linear or not. If it is linear, write the equation.
(3
points each)
12)
x 0
4
8 12
y 11 14 17 18
Up by 1
Up by 4
Up by 3
x 3
4
5
6
y 19 25 31 37
13)
Up by 6
y  a  bx
19  a  6(3)
19  a  18
Linear? YES
Linear? YES
Equation: y = ¾x + 11
Equation: y = 6x + 1
1 a
In order to most effectively prepare for these same problems on Friday’s test,
the best thing you can do is carefully check over your answers. If your answer
is correct, and your work seems good, then give yourself those points and
move on. If, however, your answer is wrong, carefully study the work shown
on this answer key to determine where your mistake occurred. It’s likely that a
simple arithmetic error in an otherwise well-done problem would get you at
least partial credit.
For any problem that you do wrong (more than just an absent-minded
mistake), the best thing you can do is go back into that section of notes and
review what should be done, then re-do notes/homework problems. Also
make sure that something about that problem appears on your note card!