Name _________________________________________________ Class _______________ Date _______________
Practice
6-6
Solving Systems of Linear Equations Using Subtraction
6-6
Solving Systems of Linear Equations Using Subtraction
1.Find the best algebraic method to solve the given system by inspecting the
equations.
2x - 4y = - 2
- 6x + 4y = - 14
❍❍ A.subtraction
❍❍ B.addition
❍❍ C.substitution
2.Which of these systems of equations would be best solved using the
subtraction method? Check all that apply.
I.
3x – 4y = 0 II. 2y = x – 2 III. –4x + 3y = 0
–4x – 9y = –36
–9x + 4y = –36
y = 3x – 7
❑❑ A. System III
❑❑ B. System II
❑❑ C. System I
3.Solve the system of equations using subtraction.
2x - 7y = - 13
8x - 7y = 11
4.Solve the system of equations using subtraction.
2x - 2y = - 4
2x + y = 11
5.At a basketball game, a team made 56 successful shots. They were a
combination of 1- and 2-point shots. The team scored 94 points in all. Write
and solve a system of equations to find the number of each type of shot.
6.Yesterday, a movie theater sold 279 bags of popcorn. A large bag of popcorn
costs $4. A small bag of popcorn costs $1. In all, the movie theater made $567
from popcorn sales. Write and solve a system of equations to find how many
bags of each size of popcorn were sold.
7.a)Writing Solve the system of equations using subtraction.
x+ y = 3
x–y= 1
b) Describe two different ways to solve the system.
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Practice 6-6
1
Homework G
8.a)Reasoning Which is the best algebraic method to solve the given system by
inspecting the equations?
3x - 6y + 2y = - 1
3x + 3x + 4y = 46
❍❍ A.substitution
❍❍ B.addition
❍❍ C.subtraction
b) Explain your reasoning.
9. Error Analysis A student incorrectly claimed the solution of this system of
equations is (4, –2).
4x – 5y = 6
6x – 5y = 14
a) What is the correct solution?
b) What mistake might the student have made?
❍❍ A. The signs on the x- and y-coordinates are incorrect.
❍❍ B. The sign on the x-coordinate is correct, but the sign on the
y-coordinate is incorrect.
❍❍ C. The student switched the x- and y-coordinates.
❍❍ D. The sign on the y-coordinate is correct, but the sign on the
x-coordinate is incorrect.
10. Age If you add Natalie’s age and Fred’s age, the result is 44. If you add Fred’s
age to 3 times Natalie’s age, the result is 70. Write and solve a system of
equations to find how old Fred and Natalie are.
11. Estimation The perimeter of a rectangle is about 19.8 cm. If you double the
width of the rectangle the perimeter is about 26.2 cm. Find the dimensions of
the smaller rectangle. Round the given values to the nearest integer. Use the
rounded values to write and solve a system of equations to find the length
and the width of the rectangle.
12. Two airplanes are carrying food and medical supplies to a country in need.
One airplane is carrying 61 meals and 59 medical kits. The total cost for the
supplies on that airplane is $777. The other airplane is carrying 75 meals and
59 medical kits. The total cost for the supplies on that airplane is $847.
a) Write and solve a system of equations to find the price of one meal and
the price of one medical kit.
b) If a third airplane is carrying 70 meals and 63 medical kits, what is the total
cost of supplies?
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Practice 6-6
2
Homework G
13. Solve the system of equations using subtraction.
- 8x + 4x + 2y = - 6
- 4x + 2y - 8y = - 54
14. Challenge Solve the system of equations using subtraction.
3x - 8y = 7 - 6y
6x - 2y = 31 - 3x
15. Challenge A car repair shop charges $1 for mounting a tire purchased from
the shop. The repair shop charges $7 for mounting a tire that was purchased
from another shop. Last month, the total charges for mounting tires were
$812. The number of tires mounted and purchased from the shop was 440
less 3 times the number of tires mounted that were purchased from other
shops. Write and solve a system of equations to find the number of tires
purchased from the shop and from other shops.
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Practice 6-6
3
Homework G
ANSWER
KEY
Practice 6-6: Solving Systems of Linear Equations Using
Subtraction
1.B
2.A
3.(4, 3)
4.(3, 5)
5.2-point shots: 38
1-point shots: 18
6.large bags of popcorn: 96
small bags of popcorn: 183
7.a)(2, 1)
b)
Answers will vary
8.a)B
b)
Answers will vary
9.a)(4, 2)
b)
B
10. Fred: 31 years old
Natalie: 13 years old
11. length: 7 cm
width: 3 cm
12. a) meal: $5
medical kit: $8
b)
$854
13. (4.5, 6)
14. (4, 2.5)
15. tires purchased from the shop: 161
tires purchased from other shops: 93
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Practice 6-6
4
Answer Key G