To solve this system of equations, we can use the substitution method.

First, let's solve the first equation:

5(3x+2)=7+12y
15x + 10 = 7 + 12y
15x + 10 - 7 = 12y
15x + 3 = 12y
y = (15x + 3) / 12
y = (5x + 1)

Now, substitute y = (5x + 1) into the second equation:

4(x + (5x + 1)) + x = 31
4(6x + 1) + x = 31
24x + 4 + x = 31
25x + 4 = 31
25x = 27
x = 27 / 25
x = 1.08

Now, substitute x = 1.08 back into y = (5x + 1):

y = 5(1.08) + 1
y = 5.4 + 1
y = 6.4

Therefore, the solution to the system of equations is:
x ≈ 1.08
y ≈ 6.4