Answer:
{a,c,d,b} = {49/16,29/16,2,-31/48}
Step-by-step explanation:
[1] 3a + c - 4d = 3
[2] -4a + 4c + d = -3
[3] -a - 2d + 3b = -9
[4] - d = -2
// Solve equation [4] for the variable d
[4] d = 2
// Plug this in for variable d in equation [1]
[1] 3a + c - 4•(2) = 3
[1] 3a + c = 11
// Plug this in for variable d in equation [2]
[2] -4a + 4c + (2) = -3
[2] -4a + 4c = -5
// Plug this in for variable d in equation [3]
[3] -a - 2•(2) + 3b = -9
[3] -a + 3b = -5
// Solve equation [1] for the variable c
[1] c = -3a + 11
// Plug this in for variable c in equation [2]
[2] -4a + 4•(-3a+11) = -5
[2] -16a = -49
// Solve equation [2] for the variable a
[2] 16a = 49
[2] a = 49/16
// Plug this in for variable a in equation [3]
[3] -(49/16) + 3b = -5
[3] 3b = -31/16
[3] 48b = -31
// Solve equation [3] for the variable b
[3] 48b = - 31
[3] b = - 31/48
// By now we know this much :
a = 49/16
c = -3a+11
d = 2
b = -31/48
// Use the a value to solve for c
c = -3(49/16)+11 = 29/16
