The system of equations to be solved is:

3a + b + c + 2d = 4 ...(1)

8a + 2b + 5c + d = 11 ...(2)

a + 3b + 4c + 3d = 13 ...(3)

2a + 4b + c + d = 18 ...(4)

First let's eliminate one of the variables

(1) - (4)

=> a - 3b + d = -14 ...(5)

(2) - 5*(4)

=> -2a - 18b - 4d = -79 ...(6)

(3) - 4*(4)

-7a - 13b - d = -59 ...(7)

Again eliminate one variable

(5) + (7)

=> -6a -16b = -73 ...(8)

(6) + 4*(5)

=> 2a - 30b = -135 ...(9)

(8) + 3*(9)

=> -106b = -478

b = 239/53

a = (-135 + 30*(239/53))/2 = 15/106

d = -14 - a + 3b = -65/106

c = 18 - 2a - 4b - d = 31/106

The solution of the system of equations is a = 15/106, b = 239/53, c = 31/106 and d = -65/106