Name ———————————————————————
LESSON
6.3
Date ————————————
Practice A
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. 3x 2 y 5 23
2. 8x 5 y 1 1
y 1 8x 5 11
3y 1 8x 5 7
4. 7x 2 y 5 13
5. 14 5 x 2 3y
y 5 14x 2 3
x 1 10y
0 5 23
3. 7x 2 4y
4 58
4 5 27x 1 9
4y
6. 8x 1 1 5 4y
4
4 1 3 5 14x
4y
Describe the first step you would use to solve the linear system.
7. x 1 4y
4 51
6x 2 4y
4 5 23
10. 24x 2 4y
4 57
4 2x52
4y
8. 2x 1 3y 5 21
3y 5 22x 1 3
11. 6x 2 4y
4 55
26x 2 55y 5 7
9. 5x 1 y 5 8
x 1 y 5 26
12. 3x 5 y 2 9
25x 1 y 5 8
Solve the linear system by using elimination.
14. x 1 4y
4 59
3x 1 y 5 4
2x 2 2y
2 53
16. 2x 1 y 5 7
17. 4x 1 3y 5 18
x1y51
19. 3x 5 y 1 5
2x 1 y 5 5
22. 6x 2 3y 5 36
5x 5 3y 1 30
4x 2 2y
2 58
20. x 2 4y
4 5 219
3y 2 15 5 x
23. 24x 1 y 5 227
2y 1 6x 5 43
15. 5x 2 3y 5 214
x 1 3y 5 2
18. 25x 1 2y
2 5 22
3x 1 2y
2 5 210
21. y 2 3 5 22x
2x 1 3y 5 13
24. 9x 2 4y
4 5 255
3x 5 24y
4 2 21
25. Rollerblading One day, you are rollerblading on a trail while it is windy. You travel
LESSON 6.3
along the trail, turn around and come back to your starting point. On your way out
on the trail, you are rollerblading against the wind. On your return trip, which is the
same distance, you are rollerblading with the wind. You can only travel 3 miles an
hour against the wind, which is blowing at a constant speed. You travel 8 miles an
hour with the wind. Use the models below to write and solve a system of equations
to find the average speed when there is no wind and the speed of the wind.
6-30
Against the wind: Your speed with no wind 2 Speed of wind 5 Your speed
With the wind: Your speed with no wind 1 Speed of wind 5 Your speed
26. Car Wash A gas station has a car wash. If you get your gas tank filled, then you are
charged a lower flat fee x in dollars for a car wash plus y dollars per gallon for the
gasoline. Two cars fill up with regular gasoline and both get a car wash. One car uses
8 gallons of gasoline and pays $22.80 for the gas and car wash and the other car uses
6 gallons of gasoline and pays $18.60 for the gas and car wash. Find the fee for the
car wash and the cost of one gallon of regular gasoline.
Algebra 1
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
13. 6x 2 y 5 5
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