Name:
Additional Exercises 5.1
Date:
Decide which ordered pair, if any, is a solution of each system of equations.
1. y = 6x – 25
3x + y = 11
1. ____________________________
(a) (3, −7)
(b) (4, −1)
(c) (5, −4)
2. y = 4x + 9
3x – 5y = 6
2. ____________________________
(a) (−1, 5)
(b) (2, 0)
(c) (−3, −3)
3. y = 2x – 10
9x + 4y = –6
3. ____________________________
(a) (2, −6)
(b) (2, −6)
(c) (5, 0)
4. Does (7, −2) satisfy the system of linear equations? Answer yes or no. 4. ____________________________
3x + 8y = 5
y=x+9
5. Does (−3, 4) satisfy the system of linear equations? Answer yes or no. 5. ____________________________
2x + 5y = 14
y=x+1
6. Does ⎛⎜ 2 , − 1 ⎞⎟ satisfy the system of linear equations? Answer yes or no. 6. ____________________________
⎝3
4⎠
9x + 8y = 4
3x + 12y = –1
Identify each system as consistent, inconsistent, or dependent. State whether the system has exactly one solution, no
solution or an infinite number of solutions.
y
7. ____________________________
7.
4
1
2
2
−4
−2
−2
2
4
x
−4
y
8.
8. ____________________________
4
2
1
−4
−2
−2
2
4
x
−4
2
y
9.
1
9. ____________________________
2
4
2
−4
−2
−2
2
4
x
−4
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169
Additional Exercises 5.1 (cont.)
Name:
Express each equation in slope-intercept form. Then determine, without graphing the equations, whether the system
has exactly one solution, no solution or an infinite number of solutions.
10. 2x + 3y = –11
–3x – 4y = 16
10. ____________________________
11. 3x – 4y = 3
3x – 4y = 10
11. ____________________________
12. –4x + 2y = 12
x – 2y = –9
12. ____________________________
13. 3x + 2y = 0
9x + 6y = 0
13. ____________________________
14. 3x + 4y = –9
3x + 4y = –1
14. ____________________________
15. –3x + 2y = 5
–4x + y = 10
15. ____________________________
Determine the solution to each system graphically. If the system is dependent or inconsistent, so state.
16.
4x + y = 4
1
x = 1− y
4
16. ____________________________
y
x
17.
x + y = −1
17. ____________________________
y = 2x + 8
y
x
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170
Additional Exercises 5.1 (cont.)
18.
x+ y = 4
Name:
18. ____________________________
y = 3x − 4
y
x
19.
2y = x
1
y = x −3
2
19. ____________________________
y
x
20.
x − 2 y = −2
20. ____________________________
x = −2 + 2 y
y
x
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171
Name:
Additional Exercises 5.2
Date:
Find the solution to each system of equations using substitution.
1. 2x + 5y = –10
y = –3x + 11
1. ____________________________
2. 5x – 3y = 19
y = 2x – 7
2. ____________________________
3. 6x + 5y = 14
2x – 3y = 42
3. ____________________________
4. 3x + 6y = 15
x = –2y + 1
4. ____________________________
5. –4x – y = –26
–7x – 7y = –35
5. ____________________________
6. x + 2y = –5
y = 3x + 1
6. ____________________________
7. 9x – 5y = 2
–4x – 9y = –8
7. ____________________________
8. 6x + 6y = –3
y = –x
8. ____________________________
9. 6x – 4y = 16
7x + 7y = 112
9. ____________________________
10. 3x + 2y = 0
x – 2y = 3
10. ____________________________
11. 3x + 4y = 6
y = 4x + 11
11. ____________________________
12. 2x + 3y = 22
x – 3y = –7
12. ____________________________
13. 3x – 4y = 8
y = –x + 5
13. ____________________________
14. –5x – y = 1
4x + 8y = –5
14. ____________________________
15. 4x + 4y = –3
y = –x
15. ____________________________
16. 7x + 5y = –24
–6x – 5y = 27
16. ____________________________
17. –4x – y = 4
1
x = –1 − y
4
17. ____________________________
18. x + 4y = 11
y = 4x + 7
18. ____________________________
19. x – 2y = –8
x – 2y = 7
19. ____________________________
20. 2x + y = 2
–x – y = 1
20. ____________________________
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172
Name:
Additional Exercises 5.3
Date:
Solve each system of equations using the addition method.
1. x – 2y = 13
3x + 2y = 15
1. ____________________________
2. –2x + y = 8
3x + 4y = –12
2. ____________________________
3. –4x + 2y = 14
2x + y = 3
3. ____________________________
4. 4x + y = 2
10x – 5y = –1
4. ____________________________
5. 2x – y = 4
x+y=5
5. ____________________________
6. 4x – 3y = 1
3x – 4y = 4
6. ____________________________
7. 4x + 7y = –49
–5x – 5y = 50
7. ____________________________
8. 2x – 3y = –21
3x + 3y = 6
8. ____________________________
9. 2x + 3y = 3
x – 4y = –4
9. ____________________________
10. 8x + 3y = –16
–4x + 4y = –36
10. ____________________________
11. 3x – 4y = 3
5x + 4y = 10
11. ____________________________
12. 4x – 3y = 11
3x + 3y = –18
12. ____________________________
13. 3x – 4y = 3
9x – 12y = 9
13. ____________________________
14. 3x + 2y = 0
3x + 2y = 3
14. ____________________________
15. 7x – 3y = –3
6x + 4y = 3
15. ____________________________
16. 4x – 3y = 3
5x – 2y = 4
16. ____________________________
17. 8x – 2y = 70
–5x + 9y = –67
17. ____________________________
18. x – 2y = –8
2x – 4y = –16
18. ____________________________
19. y = –2x + 13
3x + y = 20
19. ____________________________
20. 3x + 2y = 0
3x – 2y = 0
20. ____________________________
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173
Name:
Additional Exercises 5.4
Date:
Express each exercise as a system of linear equations, and then find the solution.
1. The sum of two integers is 52. Find the numbers if one number is
2 greater than the other.
1. ____________________________
2. The difference of two integers is 8. Find the two numbers if the
larger is one more than twice the smaller.
2. ____________________________
3. Two angles are supplementary when the sum of their measures is
180°. If angles A and B are supplementary angles and angle A is
five times as large as angle B, find the measure of each angle.
3. ____________________________
4. If angles A and B are supplementary angles and angle A is 56°
greater than angle B, find the measure of each angle.
4. ____________________________
5. A rectangular garden will be bordered by 16 yards of decorative
fencing. What dimensions will the garden have if the length is
to be 2 yards greater than the width?
5. ____________________________
6. Pat has 48 inches of trim for each rectangular placemat he wants
to make. What dimensions will each placemat have if the length
is to be twice the width?
6. ____________________________
7. Tickets to a local movie were sold at $5.00 for adults and $3.50 for
students. If 370 tickets were sold for a total of $1415.00, how many
adult tickets were sold?
7. ____________________________
8. Saver Rent a Car Agency charges $51 per day plus 20 cents per mile
to rent a certain car. Local charges $65 per day plus 16 cents per mile
to rent the same car. How many miles will have to be driven for the
cost of Saver's car to equal the cost of Local's car?
8. ____________________________
9. Mrs. Garcia invests a total of $6331 in two savings accounts. One
account yields 8.5% simple interest and the other 8% simple
interest. Find the amount placed in each account if a total
of $517.68 in interest is received after one year.
9. ____________________________
10. The Modern Grocery has cashews that sell for $4.50 per pound
and peanuts that sell for $2.50 per pound. How much of each must
Albert, the grocer, mix to get 80 pounds of a mixture that he can
sell for $3.00 per pound?
10. ____________________________
11. How many liters of a 40% salt solution must be added to 4 liters of a
10% salt solution to obtain a 30% salt solution?
11. ____________________________
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174
Additional Exercises 5.4 (cont.)
Name:
12. Hearts Rent-a-Car Agency charges $50 per day plus 18 cents per
mile to rent a certain car. Mavis Car Rentals charges $64 per day
plus 11 cents per mile to rent the same car. How many miles will
have to be driven for the cost of the Hearts car to equal the cost of
the Mavis car?
12. ____________________________
13. Mrs. Wong invests a total of $9623 in two savings accounts. One
account yields 9% simple interest and the other 10% simple
interest. Find the amount placed in each account if a total of
$914.39 in interest is received after one year.
13. ____________________________
14. The Modern Grocery has cashews that sell for $5.00 a pound
and peanuts that sell for $2.00 a pound. How much of each
must Albert, the grocer, mix to get 120 pounds of a mixture
that he can sell for $3.00 per pound?
14. ____________________________
15. Tickets to a local movie were sold at $8.00 for adults and $5.00 for
students. If 600 tickets were sold for a total of $4116, how many
adult tickets were sold?
15. ____________________________
16. How many gallons each of 10% chloride solution and 30% chloride
solution should be mixed in order to obtain 10 gallons of 25%
chloride solution?
16. ____________________________
17. Mr. Sung invests a total of $13,649 in two savings accounts. One
17. ____________________________
account yields 8% simple interest and the other 9.5% simple interest.
Find the amount placed in each account if a total of $1175.02 in
interest is received after one year.
18. The Modern Grocery has cashews that sell for $3.50 a pound and
peanuts that sell for $2.00 a pound. How much of each must
Albert, the grocer, mix to get 60 pounds of a mixture that he can
sell for $3.00 per pound?
18. ____________________________
19. Phillipe Rodriguez and Maria Gonzales go jogging along the same
trail. Phillipe starts 0.25 hours before Maria. If Phillipe jogs at a rate
of 6 miles per hour and Maria jogs 7 miles per hour, how long after
Maria starts would it take for Maria to catch up to Phillipe?
19. ____________________________
20. Olga Marx and Karl Draginoff go jogging along the same
trail. Olga starts 0.2 hours before Karl. If Olga jogs at a rate of
5 miles per hour and Karl jogs at 7 miles per hour, how long after
Olga starts would it take for Karl to catch up to Olga?
20. ____________________________
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Name:
Additional Exercises 5.5
Date:
Determine the solution to the system of inequalities.
1.
x > –3
y ≥ –2
1.
y
x
2.
x≤1
2.
y
y > –5
x
3.
x > –1
y < –2x
3.
y
x
4.
2y > x
x≤2
4.
y
x
5.
y≥x–2
3x + y ≥ –6
5.
y
x
6.
x + 3y ≤ 3
x – 3y ≥ –6
6.
y
x
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176
Additional Exercises 5.5 (cont.)
7.
y≥x+2
y ≤ –2x + 3
Name:
7.
y
x
8.
y<x+4
3x + y ≤ 0
8.
y
x
9.
3x + 2y ≤ 4
x – y > –1
9.
y
x
10.
y > 2x – 1
y ≤ –x – 2
10.
y
x
11.
y≤x+1
2x + y < 4
11.
y
x
12.
x+y<2
x – y > –1
12.
y
x
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177
Additional Exercises 5.5 (cont.)
13.
y ≥ –x – 4
y ≤ 2x – 2
Name:
13.
y
x
14.
x + 2y ≤ 2
x – 3y ≥ –9
14.
y
x
15.
y>x+1
y < –2x + 3
15.
y
x
16.
y>x+3
2x + y ≥ –4
16.
y
x
17.
2x + 3y ≥ 6
y < 2x – 1
x<3
17.
y
x
18.
3x + 4y > 8
x≤y
x ≥ –2
18.
y
x
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Additional Exercises 5.5 (cont.)
19.
4x + 3y > –6
y>x
y<4
Name:
19.
y
x
20.
5x – 2y ≤ 4
y ≥ –x
y≥2
20.
y
x
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