Name:
Date:
Algebra I
Keystone Prep
Directions: Solve the following systems of equations by substitution
1.
x  6  4 y

2 x  3 y  1
2.
4 x  3 y  0

2 x  y  2
3.
 x  2 y  6

8 x  y  31
4.
6 x  y  35

5 x  2 y  35
Directions: Solve the following systems of equations by elimination
5.
 x  3 y  9

8 x  4 y  32
6.
3x  3 y  18

4 x  y  14
7.
5 x  4 y  20

7 y  4 x  16
8.
2 y  5 x  34

3x  2 y  46
Page 1
Mr. S. Cella
Murray Avenue M.S.
9. Write a system of inequalities for the following graph:
Inequality #1: _________________
Inequality #2: _________________
Inequality #3: _________________
10. Johnny always leaves a tip of between 8% and 20% for the server when he pays for
his dinner. This can be represented by the system of inequalities shown below,
where y is the amount of tip and x is the cost of dinner.
y > 0.08x
y < 0.2x
Which of the following is a true statement?
a) When the cost of dinner (x) is $10, the amount of tip (y) must be between $2
and $8.
b) When the cost of dinner (x) is $15, the amount of tip (y) must be between
$1.20 and $3.00.
c) When the amount of tip (y) is $3, the cost of dinner (x) must be between $11
and $23.
d) When the amount of tip (y) is $2.40, the cost of dinner (x) must be between $3
and $6.
11. A landscaping company placed two orders with a nursery. The first order was for 13
bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and
totaled $232. The bills do not list the per-item price. What were the costs of one bush and
of one tree?
Page 2
Mr. S. Cella
Murray Avenue M.S.
12. An apple farm owner is deciding how to use each day’s harvest. She can use the
harvest to produce apple juice or apple butter. The information she uses to make the
decision is listed below.
- A bushel of apple will make 16 quarts of apple juice.
- A bushel of apple will make 20 pints of apple butter.
- The apple farm can produce no more than 180 pints of apple butter
each day.
- The apple farm harvests no more than 15 bushels of apples each day.
The information given can be modeled with a system of inequalities. When x is
the number of quarts of apple juice and y is the number of pints of apple butter,
two of the inequalities that model the situation are
and
a) Write two more inequalities to complete the system of inequalities modeling
the information.
Inequality #1: __________________
Inequality #2: ___________________
b) Graph the solution set of the inequalities from Part A below. Shade the area
that represents the solution set.
c) The apple farm makes a profit of $2.25 on each pint of apple butter and $2.50
on each quart of apple juice. Explain how you can be certain the maximum
profit will be realized when the apple farm produces 96 quarts of apple juice
and 180 pints of apple butter.
Page 3
Mr. S. Cella
Murray Avenue M.S.
13. A passenger jet took three hours to fly 1800 miles in the direction of the jetstream.
The return trip against the jetstream took four hours. What was the jet's speed in still air
and the jetstream's speed?
14. The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a
certain day, 2200 people enter the fair and $5050 is collected. How many children and
how many adults attended?
15. Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher
minus one small pitcher constitutes 2 cups of water. How many cups of water can each
pitcher hold?
16. Anna burned 15 calories per minute running for x minutes and 10 calories per minute
hiking for y minutes. She spent a total of 60 minutes running and hiking and burned 700
calories. The system of equations shown below can be used to determine how much time
Anna spent on each exercise.
15x  10 y  700

 x  y  60
What is the value of x, the minutes Anna spent running?
17. Samantha and Maria purchased flowers. Samantha purchased 5 roses for x dollars
each and 4 daisies for y dollars each and spent $32 on the flowers. Maria purchased 1
rose for x dollars and 6 daises for y dollars each and spent $22. The system of equations
shown below represents this situation. Which statement is true?
5 x  4 y  32

 x  6 y  22
a) A rose costs $1 more than a daisy
b) Samantha spent more on daisies than she did on roses
c) Samantha spent $4 on each daisy
d) Samantha spend over 4 times as much on daisies as she did on roses.
Page 4
Mr. S. Cella
Murray Avenue M.S.