97-34=63-3?=37
This solution assumes that the digits do not represent their face values but are symbolic of other digits.
This table replaces the digits by symbols A-F where F is the unknown represented by ?:
3 4 6 7 9 ?
A B C D E F
Symbolically: ED-AB=CA-AF=AD where the letters replace the digits.
Arithmetically: 10E+D-10A-B=10C+A-10A-F=10A+D
Therefore:
10E+D=10A+D+10A+B; 10E=20A+B; B=0 and E=2A
20A+D-10A=10C-9A-F
19A+D=10C-F, 19A+F+D=10C
Table the possible values and extract the best:
| A |
E |
D+F |
D/F |
F/D |
C |
| 1 |
2 |
11 |
2 |
9 |
3 |
| 1 |
2 |
11 |
3 |
8 |
3 |
| 1 |
2 |
11 |
4 |
7 |
3 |
| 1 |
2 |
11 |
5 |
6 |
3 |
| 2 |
4 |
12 |
3 |
9 |
5 |
| 2 |
4 |
12 |
4 |
8 |
5 |
| 2 |
4 |
12 |
5 |
7 |
5 |
| 3 |
6 |
13 |
4 |
9 |
7 |
| 3 |
6 |
13 |
5 |
8 |
7 |
| 3 |
6 |
13 |
6 |
7 |
7 |
| 4 |
8 |
14 |
5 |
9 |
9 |
| 4 |
8 |
14 |
6 |
8 |
9 |
| 4 |
8 |
4 |
1 |
3 |
8 |
| 3 |
6 |
3 |
1 |
2 |
6 |
If we ignore duplicates and use the given digits as much as possible we can regard this as the "best" (highlighted in bold print).
The result of extracting the "best":
34679?
ABCDEF
307469
307964
So ?=4 or 9;
Recoding:
97-34=63-3?=37 stands for
64-30=73-39=34 or
69-30=73-34=39
(3 retains its face value; 9 becomes 6; 7 becomes 4 or 9; 4 becomes 0; 6 becomes 7.)
This may not be the intended solution, but it fits the equations!