First, let's simplify the first equation:

49у - 31(х + у) = 14 - 27х
49у - 31х - 31у = 14 - 27х
18у - 31х = 14 - 27х
18у = 14 - 27х + 31х
18у = 4x + 14

Now, let's simplify the second equation:

13(х - у) + 14у = 12х + 13
13x - 13y + 14y = 12x + 13
13x + y = 12x + 13

Now we have the system of equations:

1) 18у = 4x + 14
2) 13x + y = 12x + 13

We can solve this system of equations by substituting the value of y from equation 1) into equation 2):

18(4x + 14) = 13x + 13
72x + 252 = 13x + 13
59x = -239
x = -4

Now, substitute x = -4 back into equation 1) to solve for y:

18y = 4(-4) + 14
18y = -16 + 14
18y = -2
y = -1

Therefore, the solution to the system of equations is x = -4 and y = -1.