1) 23x + 4y - 7x = -3y + 15
Simplify the equation:
16x + 4y = -3y + 15
Rearrange the terms:
16x + 7y = 15

2) 31x + 28y = 1460

3) 87x - 64y = 3

4) 56x + 72y = 40

5) 15x - 51y = 16

6) 3x + 4y = 7

7) 12x + 18y = 50

8) 25x + 95y = 970

9) 102x + 1003y = 1

These are Diophantine equations, which are a type of equation where the solutions are integers only. Each equation needs to be solved individually to find the values of x and y that satisfy the equation.