Algebra 1: Systems of Equations and Inequalities
Name: _________________________
Warm-up:
Erica works in a soda-bottling factory. As bottles roll past her
on a conveyer belt, she puts caps on them. Unfortunately, Erica
sometimes breaks a bottle before she can cap it. She gets paid 4
cents for each bottle she successfully caps, but her boss deducts
2 cents from her pay for each bottle she breaks.
Erica is having a bad morning. Fifteen bottles have come her
way, but she has been breaking some and has only earned 6
cents so far today. How many bottles has Erica capped and
how many has she broken?
(a) Write a system of equations representing this situation. Be sure to define your variables.
(b) Solve the system of equations using:
substitution
(c) What does your solution mean relative to the situation?
elimination
Algebra 1: Systems of Equations and Inequalities
Name: _________________________
Choosing a Strategy for Solving Systems – Review for Quiz
When you have a system of equations to solve, how do you know which method to use?
1. For each system below, decide which strategy to use. That is, which method would be the most efficient,
convenient, and accurate: by Graphing, the Substitution Method, or the Elimination/Combination method? Do
not solve the systems yet. Be prepared to justify your reasons for choosing one strategy over the others.
a. 𝑥 = 4 − 2𝑦
3𝑥 − 2𝑦 = 4
e.
1
𝑥+4
2
𝑦 = −2𝑥 + 9
𝑦=
b.
3𝑥 + 𝑦 = 1
4𝑥 + 𝑦 = 2
f.
−6𝑥 + 2𝑦 = 76
3𝑥 − 𝑦 = −38
c.
𝑥 = −5𝑦 + 2
𝑥 = 3𝑦 − 2
g. 5𝑥 + 3𝑦 = −6
2𝑥 − 9𝑦 = 18
d.
h.
2𝑥 − 4𝑦 = 10
𝑥 = 2𝑦 + 5
𝑥−3=𝑦
2(𝑥 − 3) − 𝑦 = 7
2. Solve the following systems of equations using any method. Check each solution, if possible.
a. −2𝑥 + 3𝑦 = 1
2𝑥 + 6𝑦 = 2
1
𝑥+4
3
𝑥 = −3𝑦
b. 𝑦 =
c. 3𝑥 − 𝑦 = 7
𝑦 = 3𝑥 − 2
d.
𝑥 + 2𝑦 = 1
3𝑥 + 5𝑦 = 8
For each of the following problems. Write a system of equations to represent the situation. Then solve the
problem using any method you choose. Be sure to check your answer when you are finished.
3. The Math Club is baking pies for a bake sale. The fruit –pie recipe calls for twice as many peaches as
nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?
4. Herman and Jacquita are each saving money to pay for college. Herman currently has $1500 and is working
hard to save $2000 per month. Jacquita has $12,000 but is saving $1300 per month. In how many months will
they have the same amount of savings?
5. There are 21 animals on Farmer Cole’s farm – all sheep and chickens. If the animals have a total of 56 legs,
how many of each type of animal lives on his farm.
6. You’ve decided to give your friend a bag of marbles for her birthday. Since you know that your friend likes
green marbles better than red ones, the bag has twice as many green marbles as red. The label on the bag says it
contains a total of 84 marbles.
How many green marbles are in the bag?
7. The Alpine Music Club is going on its annual music trip. The members of the club are yodelers, and they
like to play the xylophone. This year they are taking their xylophones on a gondola to give a performance at the
top of Mount Monch.
The gondola conductor charges $2 for each yodeler and $1 for each xylophone. It costs $40 for the entire club,
including the xylophones, to ride the gondola. Two yodelers can share a xylophone, so the number of yodelers
on the gondola is twice the number of xylophones.
How many yodelers and how many xylophones are on the gondola?
8. You have 14 coins in your pocket that are either quarter or nickels. They total $2.50. How many of each
coin do you have?
9. Ms. Salinas is in charge of sales for Opportunity Company. Ms. Salinas knows that a particular task will
take 8 hours to complete. She has budgeted $80 for this task.
The supervisor is paid $15 an hour. Her assistant is paid $7 per hour. The supervisor will start the task, so she
can plan and organize it. Then her assistant will take over and complete the task. Ms. Salinas needs to figure
out how long each person should work so the company’s costs meet her budget and time estimate.
10. A rectangle has a perimeter of 204 feet. Its length is six feet longer than twice its width. If L stand for
length of the rectangle and W stands for its width, write a system of equations that models the information given
in this problem and solve it to find the length and width of this rectangle.
11. One evening, Gemma saw three different phone-company ads. TeleTalk boasted a flat rate of $0.08 per
minute. AmeriCall charges $0.30 per call plus $0.05 per minute. CellTime charges $0.60 per call plus only
$0.03 per minute.
a.
Gemma is planning a phone call that will take about 5 minutes. Which phone plan should she use and
how much will it cost?
b.
How long would a call need to be to cost the same with TeleTalk and AmericCall? What about
AmeriCall and CellTime? Show your work and justify your solution.