To solve this equation, we can set up a system of equations:

4x - 3 = 31
6x + 2 = 4

Solving the first equation:
4x - 3 = 31
Adding 3 to both sides:
4x = 34
Dividing by 4:
x = 8.5

Plugging this value of x into the second equation:
6(8.5) + 2 = 4
51 + 2 = 4
53 = 4

This system of equations has no solution, as the second equation is not true for the value of x we found in the first equation.