Name__________________________________ Period_____________ Date___________________
7.1 – Solving Systems of Equations
Solve each system by graphing.
1) y = 2x – 3
y=x–1
2) -4y = x + 4
1
x + y = -1
4
3) x = 10
y = -7
Solve each system by substitution.
4) y = x + 6.1
2x + y = -1.4
5) x + y = 6
5x + 5y = 10
Solve each system by elimination.
6) 5x – 6y = -32
3x + 6y = 48
7) x + 3y = 7
x – 4y = 14
Solve each system using the method of your choice.
8) 5a + 6b = 54
3a – 3b = 17
9) 2p – 5q = 6
4p + 3q = -1
10) 3x – 2y = 6
5x + 7y = 41
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Write a system of equations for the following problems, then solve using any method. If you
graph, you must note this in your work.
11) Suppose you and your friends form a band, and the band wants to record a demo
tape. Studio A rents for $100 plus $50/hour. Studio B rents for $50 plus $75/hour. If h
represents the number of hours and c represents the cost, determine for what number
of hours is the cost of using either studio the same, and how much does it cost?
12) A farmer grows only soybeans and corn on his 240-acre farm. This year he wants to
plant 80 more acres of soybeans than of corn. How many acres does the farmer need
to plant of each crop?
13) You are celebrating a victory with friends at a neighborhood sandwich shop. You have
$16 to buy a total of 12 sandwiches. If a chicken sandwich costs $1.50 and a
tuna sandwich costs $1, how many of each type of sandwich could you buy?
14) You buy a personal computer that costs $1750. Your typing service charges $5 per
page. Expenses are $0.50 per page for ink, paper, electricity, and other expenses.
Determine how many pages you must type to break even.
15) Suppose you have just enough coins to pay for a loaf of bread priced at $1.95. You
have a total of 12 coins in quarters and dimes. How many of each coin do
you have?
16) The Drama Club sold tickets to their latest production of Grease. The cost of an adult’s
ticket was $5, and the cost of a student’s ticket was $3. If the club made $2735 and
sold 765 tickets, how many of each type of ticket did they sell?
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