The following system of equations has to be solved for a, b, c, d:

a+b+c+d = 8 ...(1)

a- b+c + d = 2 ...(2)

a - b - c - d = 10 ...(3)

a + b + c - d = 1 ...(4)

Add (1) and (3)

a + b + c + d + a - b - c - d = 10 + 8

=> 2a = 18

=> a = 9

Subtract (4) from (1)

a + b + c + d - (a + b + c - d) = 8 - 1

=> 2d = 7

=> d = 7/2

Substitute a = 9 and d = 7/2 in (2) and (3)

9- b+c + 7/2 = 2

=> -b + c = -21/2 ...(5)

9 - b - c - 7/2 = 10

=> -b - c = 9/2 ...(6)

Add (5) and (6)

=> -2b = -6

=> b = 3

c = -3 - 9/2 = = -15/2

**The solution of the system of equation is a = 9, b = 3, c = -15/2 and d = 7/2**