Chapter 7 continued - NOHS Teachers

Chapter 7 continued
28.
y
3
1
1
x
2x 10y > 8
10y > 2x 8
y < 1 5 x 4 5
x 5y < 12
Chapter 7 Test (p. 443)
1. y 2x 3
y
y 2x 1
y 2x 1
29.
3
y
9
5y < x 12
y > 1 5 x 12 5
x 3y ≤ 15
3y ≤ x 15
1
4
(1, 1)
x
30.
3
9 3
3
y
1
1 1 3
1
3
6
x
x
y ≤ 1 3 x 5
9x ≥ 27
x ≥ 3
x 2y > 4
2y > x 4
y > 1 2 x 2
2.
Check:
Solution: 1, 1
6x 2y 16
y 2x 3
1 ? 21 3
1 1
2y 6x 16
y 3x 8
y 2x 1
1 ? 21 1
1 1
2x y 2
y 2x 2
5
y
31.
y
x y < 8
2
(2, 2)
6
y < x 8
2
x
2
2
2
2
6
x
x y < 0
y < x
y > x
Check: 6x 2y 16
62 22 ? 16
2x y 2
22 2 ? 2
32.
y
9
3
3
3
9
3 9 15 x
7y > 49
y > 7
7x y ≥ 14
y ≥ 7x 14
x y ≤ 10
3.
12 4 16
Solution: 2, 2
4x y 10
y 4x 10
y 4x 10
2 2
2x 4y 16
4y 2x 16
y 1 2x 4
y ≤ x 10
y
(4, 6)
2
4
x
Check: 4x y 10
44 6 ? 10
16 6 10
Solution: 4, 6
2x 4y 16
24 46 16
8 24 16
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Algebra 1 175
Chapter 7 Worked-out Solution Key

Chapter 7 continued
4.
5.
6.
4x y 10 6x 2y 22
7. 4x 7y 2
y 4x 10
2y 6x 22
x y 5
y
(3, 2)
1
1
x
Check: 6x 2y 22
63 22 ? 22
18 4 22
Solution: 3, 2
3x 5y 10
5y 3x 10
y 3 5 x 2
(10, 4)
4
Check: x 2y 18
10 24 ? 18
10 8 18
Solution: 10, 4
2x 3y 12
3y 2x 12
y 2 3 x 4
y 3x 11
y x 5
y x 5
4x 7x 5 2
4x 7x 35 2
11x 33
x 3
4x y 10
8. 7x 4y 5
43 2 ? 10
x 6y 19
12 2 10
x 6y 19
76y 19 4y 5
x 2y 18
42y 133 4y 5
2y x 18
46y 138
y 1 2 x 9
y 3
y
9.
2
x
y
4
(6, 0)
2
x
11.
Solution: 1, 3
3x 6y 24
2x y 1
y 2x 1
y 2x 1
3x 62x 1 24
3x 5y 10
3x 12x 6 24
310 54 ? 10
15x 30
30 20 10
x 2
Solution: 2, 3
x 3y 6
10. 5x y 7
3y x 6
4x 8y 12
y 1 3 x 2
y 5x 7
4x 85x 7 12
4x 40x 56 12
44x 44
x 1
Solution: 1, 2
x 6y 9
Check: 2x 3y 12
26 30 ? 12
x 3y 6
6 30 ? 6
x 4y 11
x 6y 9
12 12
6 6
6y 9 4y 11
Solution: 6, 0
6y a 4y 11
10y 20
y 2
Solution: 3, 2
3 y 5
y 2
y 2
Solution: 3, 2
x 63 19
x 1
22 y 1
y 3
y 3
51 y 7
y 2
y 2
x 62 9
x 3
176 Algebra 1
Chapter 7 Worked-out Solution Key
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Chapter 7 continued
12.
Solution:
13. 6x 7y 5 Multiply by 2 →12x 14y 10
14.
4x 2y 10 Multiply by 7 →28x 14y 70
Solution:
Solution:
15. 3x 3y 12 Multiply by 4 →12x 12y 48
16.
8x 3y 0
x 9y 92
x 9y 92
89y 92 3y 0
72y 736 3y 0
8x 3 32 3 0
3 2 , 2
7x 2y 5
10x 2y 6
3x 1
x 1 3
7 1 3 2y 5
4x 2y 20
Solution: 2, 6
3x 4y 9
8x 32
x 4
4, 10 2 3
2y 8 3
y 4 3
1 3 ,4 3
Solution: 5 3, 1
x 9y 92
69y 736
y 10 2 3
Multiply by 3 →
40x 60
3x 4y 9
8y 8
y 1
3x 41 9
3x 5
x 5 3
x 3 2
6 3 2 7y 5
7y 14
y 2
12x 6y 60
4y 3x 1 Rearrange → 3x 4y 1
18y 108
y 6
3x 36 12
3x 6
x 2
17. 8x 2 y 0 Rearrange → 8x y 2
Solution: 13, 102
18. 5y 3x 1 Multiply by 2 →10y 6x 2
4y 2x 80 Multiply by 3 →12y 6x 240
19.
20.
21.
9x y 219
Solution: 18, 11
8x 4y 4
2x y 3 Multiply by 4 → 8x 4y 12
Exactly one solution: 1, 1
6x 3y 6
2x 6y 30 Multiply by 3 → 6x 18y 90
Exactly one solution: 3, 4
x 1 3y 6
3x y 16
x 1 3 y 6
x 1 3y 6
22. 3x y 8 Multiply by 6 → 18x 6y 48
4x 6y 6
Exactly one solution: 3, 1
9x y 219
17x 221
x 18
x 13
813 y 2
6x 34 6
x 3
3 1 3y 6 y 16
y 18 y 16
no solution
y 102
22y 242
y 11
511 3x 11
3x 54
8x 4y 4
16x 16
x 1
81 4y 4
6x 3y 6
21y 84
y 4
4x 6y 6
14x 42
33 y 8
4y 4
y 1
6x 18
x 3
y 1
18 16
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Algebra 1 177
Chapter 7 Worked-out Solution Key

Chapter 7 continued
23. 3x 4y 8 Multiply by 3 →9x 12y 24
24. 6x y 12 Multiply by 2 →
Exactly one solution: 3, 6
25. y
26.
27. y
28. x ≥ 0
3
y ≥ 0
29.
31.
9
2x 6y 12 Multiply by 2 →
infinitely many solutions
4x 2y 0
1
3
y ≤ 9
5
3
x ≤ 4
y > 2x 7
x y 6
4x 4.45y 25.80
x y 6
4y 6 4.45y 25.80
4y 24 4.45y 25.80
x 4 6
x 2
1 3
1
3
0.45y 1.80
y 4
2 bags of oyster shell grit
4 bags of sunflower seeds
x
x
30.
x ≥ 0
y ≥ 0
9x 12y 24
y ≤ 2 3x 4
x ≤ 6
2
2
2
6
0 0
12x 2y 24
4x 2y 0
8x 24
x 3
63 y 12
y 6
y
6
y ≤ 2x 5
y ≥ 2x 1
x
Chapter 7 Standardized Test (pp. 444–445)
1. D
2. C
4. A
5. E
6. E
7. B
8. B
4
5 x 1 2 y 16
x y 24
4
5y 24 1 2y 16
4 5 96 5 1 2y 16
2x 7y 8
x 6y 10
26y 10 7y 8
12y 20 7y 8
3 4 x 7 10 y 5 y 12
5
1
4x 10y 3 5 Multiply by 3 →
35x 2 15x 6
x y 42
5x 2y 150
5y 42 2y 150
5y 210 2y 150
4x 2y 6
x y 24
3
10y 16 5
y 32 3
x 6y 10
5y 12
x y 42
3y 60
y 20
3. C
7x y 15 Multiply by 2 → 14x 2y 30
9. B 10. A 11. D 12. C
x y 15
x y 19
x y 15
y 15 y 19
x 17 15
2y 34
x 2
y 17
2x 7 12 5 8
2x 84 5 8
2x 44
5
22 5 12
5 2
x 22 5
3 4x 7 10y 5
3
4 x 9 10 y 15
1 5 y 10
y 50
3 4x 7 1050 5
3 4 x 35 5
x 40
x y 40 50 90
4x 2y 6
18x 36
x 2
42 2y 6
2y 2
y 1
178 Algebra 1
Chapter 7 Worked-out Solution Key
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