This algebra worksheet challenges students to solve for y across twenty different linear equations.

I'll solve each equation step by step to find the value of y.

Equations 1-10 (simple multiplication):

1. 3y = 27
Divide both sides by 3: y = 9

2. 9y = 81
Divide both sides by 9: y = 9

3. 12y = 132
Divide both sides by 12: y = 11

4. 6y = 72
Divide both sides by 6: y = 12

5. 20y = 120
Divide both sides by 20: y = 6

6. 15y = 75
Divide both sides by 15: y = 5

7. 10y = 160
Divide both sides by 10: y = 16

8. 9y = 72
Divide both sides by 9: y = 8

9. 11y = 88
Divide both sides by 11: y = 8

10. 4y = 36
Divide both sides by 4: y = 9

Equations 11-20 (with addition/subtraction):

11. 5y + 15 = 65
Subtract 15 from both sides: 5y = 50
Divide by 5: y = 10

12. 9y + 20 = 83
Subtract 20 from both sides: 9y = 63
Divide by 9: y = 7

13. 7y + 9 = 44
Subtract 9 from both sides: 7y = 35
Divide by 7: y = 5

14. 4y + 18 = 34
Subtract 18 from both sides: 4y = 16
Divide by 4: y = 4

15. 6y + 40 = 100
Subtract 40 from both sides: 6y = 60
Divide by 6: y = 10

16. 12y - 15 = 45
Add 15 to both sides: 12y = 60
Divide by 12: y = 5

17. 8y - 22 = 42
Add 22 to both sides: 8y = 64
Divide by 8: y = 8

18. 5y - 8 = 27
Add 8 to both sides: 5y = 35
Divide by 5: y = 7

19. 11y - 13 = 53
Add 13 to both sides: 11y = 66
Divide by 11: y = 6

20. 3y - 24 = 0
Add 24 to both sides: 3y = 24
Divide by 3: y = 8

Let me verify a few answers to make sure they're correct:
- #3: 12 × 11 = 132 ✓
- #11: 5(10) + 15 = 50 + 15 = 65 ✓
- #17: 8(8) - 22 = 64 - 22 = 42 ✓
- #20: 3(8) - 24 = 24 - 24 = 0 ✓

Final Answer:
1. y = 9
2. y = 9
3. y = 11
4. y = 12
5. y = 6
6. y = 5
7. y = 16
8. y = 8
9. y = 8
10. y = 9
11. y = 10
12. y = 7
13. y = 5
14. y = 4
15. y = 10
16. y = 5
17. y = 8
18. y = 7
19. y = 6
20. y = 8