solve an xor'd linear equation

[Math_Geek]

hello,

i have 6 variables

a=5

b=10

c=7

d=9

x=1

y=2

when i solve this equation using gauss-jordan it gives me wrong answer

a⊕0⊕c⊕0⊕0⊕0=2

0⊕b⊕0⊕d⊕0⊕0=3

 

a⊕0⊕0⊕0⊕x⊕0=4

0⊕b⊕0⊕0⊕0⊕y=8

 

0⊕0⊕c⊕0⊕x⊕0=6

0⊕0⊕0⊕d⊕0⊕y=11

 

⊕ is XOR

 

thanks for your help