Download Practice B

Name ———————————————————————
LESSON
6.3
Date ————————————
Practice B
For use with the lesson “Solve Linear Systems by Adding or Subtracting”
Rewrite the linear system so that the like terms are arranged in columns.
1. 8x 2 y 5 19
y 1 3x 5 7
2. 4x 5 y 2 11
3. 9x 2 2y
2 55
6 1 4x 5 23
6y
2 5 211x 1 8
2y
Describe the first step you would use to solve the linear system.
4. 22x 2 y 5 24
5. 25 5 x 2 7y
7
y 5 6x 2 5
x 1 12y
2 5 28
7. x 1 9y
9 52
8. 4x 1 3y 5 26
14x 2 9y
9 5 24
6. 3x 1 7 5 2y
2
22y
2 2 1 5 10x
9. 4x 1 y 5 210
3y 5 25x 1 1
x 1 y 5 214
Solve the linear system by using elimination.
10. x 1 5y
5 5 28
2x 2 22y 5 213
13. 3x 5 y 2 20
27x 2 y 5 40
16. 23x 5 y 2 20
3
5
19. } x 1 y 5 2}
2
2
4x 1 y 5 25
12. 6x 1 y 5 39
3x 1 4y
4 5 10
14. 2x 2 6y
6 5 210
22x 1 y 5 217
15. x 2 3y 5 6
4x 5 10 1 6y
6
11
1
17. x 2 } y 5 }
2
2
22x 5 3y 1 33
2
18. 2} x 1 6y
6 5 38
3
x 2 6y
6 5 233
2x 1 4y
4 5 26
1
20. 7x 2 } y 5 229
3
3
29
1
21. } x 2 } y 5 2}
2
2
2
1
2x 2 }3 y 5 29
1
2}2 x 1 3y 5 33
22. Fishing Barge A fishing barge leaves from a dock and moves upstream (against
the current) at a rate of 3.8 miles per hour until it reaches its destination. After the
people on the barge are done fishing, the barge moves the same distance downstream
(with the current) at a rate of 8 miles per hour until it returns to the dock. The speed
of the current remains constant. Use the models below to write and solve a system
of equations to find the average speed of the barge in still water and the speed of the
current.
Upstream: Speed of barge in still water 2 Speed of current 5 Speed of barge
Downstream: Speed of barge in still water 1 Speed of current 5 Speed of barge
23. Floor Sander Rental A rental company charges a flat fee of x dollars for a floor
sander rental plus y dollars per hour of the rental. One customer rents a floor sander
for 4 hours and pays $63. Another customer rents a floor sander for 6 hours and
pays $87.
a. Find the flat fee and the cost per hour for the rental.
LESSON 6.3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
2y 5 25x 1 4
11. 7x 2 4y
4 5 230
b. How much would it cost someone to rent a sander for 11 hours?
Algebra 1
Chapter Resource Book
6-31
16. a 5 25, b 5 22 17. cleanups: 250 hr;
painting: 150 hr 18. x 5 16, y 5 4 19. yes; The
linear system x 1 y 5 8 and x 1 0.5y
5 5 6.4 where
x is the amount of soil and y is the amount of the
half and half mix has a solution of x 5 4.8 and
y 5 3.2. So 3.2 buckets are needed and there are 4
buckets.
Study Guide
1. (2, 24) 2. (23, 6) 3. (6, 2) 4. (3, 8)
5. (27, 6) 6. (4, 2)
1. x 1 y 5 27 2. 350x 1 475y
5 5 10,950
3. x 5 15, y 5 12 4. 15 trumpets,
12 trombones
Number of trombones
y
27
24
21
18
15
12
9
6
3
0
1. 3x 2 y 5 23 and 8x 1 y 5 11 2. 8x 2 y 5 1
4 5 8 and 7x 1 4y
4 59
and 8x 1 3y
3 5 7 3. 7x 2 4y
4. 7x 2 y 5 13 and 214x 1 y 5 23
5. x 2 3y 5 14 and x 1 10y
0 5 23
6. 8x 2 4y
4 5 21 and 214x 1 4y
4 5 23
9. Subtract the equations. 10. Arrange the
terms. 11. Add the equations. 12. Arrange the
terms.
1
4
13. (1, 1) 14. (215, 6) 15. 22, }
3
2
16. (6, 25) 17. (3, 2) 18. (24, 1) 19. (2, 1)
20. (23, 4) 21. (21, 5) 22. (6, 0) 23. (8, 5)
1
19
1
24. 2}, 2}
3
2
(15, 12)
2
25. Your speed with no wind:
5.5 mi/h; Wind speed: 2.5 mi/h 26. Car wash:
$6; One gallon of regular gasoline: $2.10
Practice Level B
0 3 6 9 12 15 18 21 24 x
Number of trumpets
1. 8x 2 y 5 19 and 3x 1 y 5 7
2. 4x 2 y 5 211 and 4x 1 6y
6 5 23
Challenge Practice
Î2
1
2 1 Î
1 2Î 236 , Î 56 2, 1 Î 236 , 2Î 56 2, 1 Î 236 , Î 56 2
15
3
1. (2, 3) 2. }, 2}
16
2
}
}
}
}
}
}
}
}
}
}
}
}
}
}
}
23
5
3. 2 } , 2 } ,
6
6
}
4. (214, 2Ï10 ), (214, Ï10 )
3. 9x 2 2y
2 5 5 and 11x 1 2y
2 5 8 4. Arrange
the terms. 5. Arrange the terms. 6. Arrange the
terms. 7. Add the equations. 8. Arrange the
terms. 9. Subtract the equations. 10. (3, 5)
11. (22, 4) 12. (7, 23) 13. (26, 2)
14. (10, 5) 15. (29, 25) 16. (3, 11)
Lesson 6.3 Solve Linear Systems
by Adding or Subtracting
17. (10, 9) 18. (15, 8) 19. (21, 21)
Teaching Guide
still water: 5.9 mi/h; Speed of current: 2.1 mi/h
23. a. Flat fee: $15; Hourly fee: $12 b. $147
1. x 1 y 5 15
x 1 5y
5 5 47
x represents the number of $1 bills and y
represents the number of $5 bills.
2. 2x 1 6y
6 5 62; the result is a linear equation
in two variables; you cannot solve the resulting
equation because there are two variables in the
4 = 232; the result is a linear
equation. 3. 24y
equation in one variable; you can solve the resulting equation because there is one variable in the
A72
Practice Level A
7. Add the equations. 8. Arrange the terms.
Real-Life Application
5.
equation. 4. Kelly has 7 $1 bills and 8 $5 bills.
By solving the equation from Question 3 for y,
you obtain y 5 8. If you substitute this value into
the equation x 1 y 5 15 and solve for x, you
obtain x 5 7.
Algebra 1
Chapter Resource Book
1
37
20. (24, 3) 21. 8, }
3
2
22. Speed of barge in
Practice Level C
1. (24, 5) 2. (8, 6) 3. (210, 3) 4. (26, 25)
5. (9, 14) 6. (21, 7) 7. (18, 18) 8. (26, 24)
9. (15, 20) 10. (3, 5) 11. (28, 24)
12. (11, 12) 13. (23, 8) 14. (9, 16)
1
12
15. (28, 27) 16. 5, }
b
2
17. (1, 2, 1);
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
ANSWERS
Lesson 6.2 Solve Linear Systems
by Substitution, continued