Grid of 64 algebra problems where students practice isolating the variable y in simple subtraction equations.

To solve for the variable $y$ in these equations, we need to isolate $y$ on one side of the equals sign. Here is the step-by-step logic used for each type of problem found in the list:

Type 1: Equations like $4 = y - 4$
* Goal: Get $y$ by itself.
* Action: Since 4 is being subtracted from $y$, we do the opposite: add 4 to both sides.
* Calculation: $4 + 4 = 8$. So, $y = 8$.

Type 2: Equations like $3 = 9 - y$
* Goal: Get $y$ positive and by itself.
* Action: First, subtract 9 from both sides to move the number away from $y$. Then, divide or multiply by -1 to make $y$ positive. Alternatively, you can just swap the numbers: if $3 = 9 - y$, then $y = 9 - 3$.
* Calculation: $9 - 3 = 6$. So, $y = 6$.

Let's apply this logic to solve all 64 problems accurately.

Row 1:
1. $4 = y - 4 \rightarrow y = 4 + 4 = 8$
2. $4 = y - 2 \rightarrow y = 4 + 2 = 6$
3. $3 = y - 2 \rightarrow y = 3 + 2 = 5$
4. $4 = y - 5 \rightarrow y = 4 + 5 = 9$

Row 2:
5. $3 = 9 - y \rightarrow y = 9 - 3 = 6$
6. $3 = 7 - y \rightarrow y = 7 - 3 = 4$
7. $4 = y - 1 \rightarrow y = 4 + 1 = 5$
8. $7 = y - 2 \rightarrow y = 7 + 2 = 9$

Row 3:
9. $1 = 8 - y \rightarrow y = 8 - 1 = 7$
10. $2 = 3 - y \rightarrow y = 3 - 2 = 1$
11. $7 = y - 1 \rightarrow y = 7 + 1 = 8$
12. $2 = 8 - y \rightarrow y = 8 - 2 = 6$

Row 4:
13. $2 = 9 - y \rightarrow y = 9 - 2 = 7$
14. $3 = 7 - y \rightarrow y = 7 - 3 = 4$
15. $8 = y - 1 \rightarrow y = 8 + 1 = 9$
16. $3 = 4 - y \rightarrow y = 4 - 3 = 1$

Row 5:
17. $2 = 9 - y \rightarrow y = 9 - 2 = 7$
18. $6 = 7 - y \rightarrow y = 7 - 6 = 1$
19. $5 = y - 3 \rightarrow y = 5 + 3 = 8$
20. $0 = 6 - y \rightarrow y = 6 - 0 = 6$

Row 6:
21. $4 = y - 3 \rightarrow y = 4 + 3 = 7$
22. $1 = 8 - y \rightarrow y = 8 - 1 = 7$
23. $4 = 7 - y \rightarrow y = 7 - 4 = 3$
24. $1 = y - 5 \rightarrow y = 1 + 5 = 6$

Row 7:
25. $3 = y - 5 \rightarrow y = 3 + 5 = 8$
26. $6 = 9 - y \rightarrow y = 9 - 6 = 3$
27. $2 = y - 5 \rightarrow y = 2 + 5 = 7$
28. $0 = y - 2 \rightarrow y = 0 + 2 = 2$

Row 8:
29. $5 = y - 3 \rightarrow y = 5 + 3 = 8$
30. $5 = 7 - y \rightarrow y = 7 - 5 = 2$
31. $1 = 5 - y \rightarrow y = 5 - 1 = 4$
32. $2 = y - 2 \rightarrow y = 2 + 2 = 4$

Row 9:
33. $1 = y - 2 \rightarrow y = 1 + 2 = 3$
34. $0 = y - 7 \rightarrow y = 0 + 7 = 7$
35. $4 = 5 - y \rightarrow y = 5 - 4 = 1$
36. $2 = y - 3 \rightarrow y = 2 + 3 = 5$

Row 10:
37. $0 = y - 9 \rightarrow y = 0 + 9 = 9$
38. $3 = 6 - y \rightarrow y = 6 - 3 = 3$
39. $2 = y - 5 \rightarrow y = 2 + 5 = 7$
40. $4 = 9 - y \rightarrow y = 9 - 4 = 5$

Row 11:
41. $4 = 6 - y \rightarrow y = 6 - 4 = 2$
42. $3 = y - 6 \rightarrow y = 3 + 6 = 9$
43. $2 = 8 - y \rightarrow y = 8 - 2 = 6$
44. $1 = y - 1 \rightarrow y = 1 + 1 = 2$

Row 12:
45. $5 = y - 1 \rightarrow y = 5 + 1 = 6$
46. $2 = 6 - y \rightarrow y = 6 - 2 = 4$
47. $6 = y - 3 \rightarrow y = 6 + 3 = 9$
48. $2 = 5 - y \rightarrow y = 5 - 2 = 3$

Row 13:
49. $3 = 4 - y \rightarrow y = 4 - 3 = 1$
50. $2 = y - 4 \rightarrow y = 2 + 4 = 6$
51. $0 = y - 3 \rightarrow y = 0 + 3 = 3$
52. $3 = y - 3 \rightarrow y = 3 + 3 = 6$

Row 14:
53. $1 = 5 - y \rightarrow y = 5 - 1 = 4$
54. $8 = y - 1 \rightarrow y = 8 + 1 = 9$
55. $1 = y - 5 \rightarrow y = 1 + 5 = 6$
56. $4 = y - 4 \rightarrow y = 4 + 4 = 8$

Row 15:
57. $7 = 8 - y \rightarrow y = 8 - 7 = 1$
58. $3 = 5 - y \rightarrow y = 5 - 3 = 2$
59. $2 = 4 - y \rightarrow y = 4 - 2 = 2$
60. $5 = y - 4 \rightarrow y = 5 + 4 = 9$

Row 16:
61. $3 = 8 - y \rightarrow y = 8 - 3 = 5$
62. $0 = 5 - y \rightarrow y = 5 - 0 = 5$
63. $6 = 8 - y \rightarrow y = 8 - 6 = 2$
64. $0 = y - 4 \rightarrow y = 0 + 4 = 4$

Final Answer:
1. 8
2. 6
3. 5
4. 9
5. 6
6. 4
7. 5
8. 9
9. 7
10. 1
11. 8
12. 6
13. 7
14. 4
15. 9
16. 1
17. 7
18. 1
19. 8
20. 6
21. 7
22. 7
23. 3
24. 6
25. 8
26. 3
27. 7
28. 2
29. 8
30. 2
31. 4
32. 4
33. 3
34. 7
35. 1
36. 5
37. 9
38. 3
39. 7
40. 5
41. 2
42. 9
43. 6
44. 2
45. 6
46. 4
47. 9
48. 3
49. 1
50. 6
51. 3
52. 6
53. 4
54. 9
55. 6
56. 8
57. 1
58. 2
59. 2
60. 9
61. 5
62. 5
63. 2
64. 4