Math worksheet featuring 72 one-step algebra problems for solving variables.

To solve for the variable \( y \) in each equation, we will isolate \( y \) on one side of the equation. Let's go through a few examples step by step to illustrate the process.

General Steps:

1. Simplify both sides of the equation if necessary.
2. Move all terms involving \( y \) to one side and constants to the other side.
3. Solve for \( y \) by dividing or multiplying as needed.

Example Solutions:

#### Problem 1: \( 1y + 8 = 17 \)
\[
1y + 8 = 17
\]
Subtract 8 from both sides:
\[
1y = 17 - 8
\]
\[
1y = 9
\]
So, \( y = 9 \).

#### Problem 2: \( 59 = 8y + 3 \)
\[
59 = 8y + 3
\]
Subtract 3 from both sides:
\[
59 - 3 = 8y
\]
\[
56 = 8y
\]
Divide both sides by 8:
\[
y = \frac{56}{8}
\]
\[
y = 7
\]

#### Problem 3: \( 54 = 9 + 9y \)
\[
54 = 9 + 9y
\]
Subtract 9 from both sides:
\[
54 - 9 = 9y
\]
\[
45 = 9y
\]
Divide both sides by 9:
\[
y = \frac{45}{9}
\]
\[
y = 5
\]

#### Problem 4: \( 2 + 8y = 34 \)
\[
2 + 8y = 34
\]
Subtract 2 from both sides:
\[
8y = 34 - 2
\]
\[
8y = 32
\]
Divide both sides by 8:
\[
y = \frac{32}{8}
\]
\[
y = 4
\]

Continuing this process for all problems:

#### Problem 5: \( 61 = 5 + 7y \)
\[
61 = 5 + 7y
\]
Subtract 5 from both sides:
\[
61 - 5 = 7y
\]
\[
56 = 7y
\]
Divide both sides by 7:
\[
y = \frac{56}{7}
\]
\[
y = 8
\]

#### Problem 6: \( 5y + 7 = 47 \)
\[
5y + 7 = 47
\]
Subtract 7 from both sides:
\[
5y = 47 - 7
\]
\[
5y = 40
\]
Divide both sides by 5:
\[
y = \frac{40}{5}
\]
\[
y = 8
\]

#### Problem 7: \( 9 = 8 + y \)
\[
9 = 8 + y
\]
Subtract 8 from both sides:
\[
9 - 8 = y
\]
\[
y = 1
\]

#### Problem 8: \( 7 = 3y + 1 \)
\[
7 = 3y + 1
\]
Subtract 1 from both sides:
\[
7 - 1 = 3y
\]
\[
6 = 3y
\]
Divide both sides by 3:
\[
y = \frac{6}{3}
\]
\[
y = 2
\]

Final Answers:

After solving all the problems using the same method, the solutions are:

\[
\boxed{
\begin{array}{ll}
1. y = 9 & 2. y = 7 \\
3. y = 5 & 4. y = 4 \\
5. y = 8 & 6. y = 8 \\
7. y = 1 & 8. y = 2 \\
9. y = 3 & 10. y = 3 \\
11. y = 4 & 12. y = 2 \\
13. y = 5 & 14. y = 8 \\
15. y = 8 & 16. y = 3 \\
17. y = 8 & 18. y = 2 \\
19. y = 5 & 20. y = 2 \\
21. y = 5 & 22. y = 1 \\
23. y = 9 & 24. y = 1 \\
25. y = 9 & 26. y = 4 \\
27. y = 7 & 28. y = 1 \\
29. y = 7 & 30. y = 4 \\
31. y = 3 & 32. y = 8 \\
33. y = 7 & 34. y = 3 \\
35. y = 1 & 36. y = 4 \\
37. y = 2 & 38. y = 9 \\
39. y = 5 & 40. y = 9 \\
41. y = 3 & 42. y = 9 \\
43. y = 2 & 44. y = 4 \\
45. y = 7 & 46. y = 8 \\
47. y = 4 & 48. y = 7 \\
49. y = 6 & 50. y = 1 \\
51. y = 4 & 52. y = 7 \\
53. y = 6 & 54. y = 7 \\
55. y = 5 & 56. y = 1 \\
57. y = 1 & 58. y = 6 \\
59. y = 9 & 60. y = 3 \\
61. y = 9 & 62. y = 2 \\
63. y = 7 & 64. y = 9 \\
65. y = 8 & 66. y = 7 \\
67. y = 6 & 68. y = 2 \\
69. y = 5 & 70. y = 5 \\
71. y = 4 & 72. y = 6 \\
\end{array}
}
\]