linear equation with two different value for all variables

Question

i have 8 equations and 8 variables

a+c=8
d+e+f=12
g+h+z=12
a+d+g=12
e+h=8
c+f+z=12
a+e+z=12
c+e+g=12

and i have two list of value for all variables :

first results:

a=8      
c=0
d=-4
e=4
f=12
g=8
h=4
z=0

second results:

a=3
c=5
d=6
e=4
f=2
g=3
h=4
z=5

if you set value of first result or second result in equation both of them are correct is that possible?!

because if i have 6 equations and 6 variable i should have only and only one value for a variable(that mean i should have one result list for equation not two) is that right?

Answer 1

I didn't check all calculation but if it is correct it means that some of the equation are dependent and thus the system has infinitely many solutions.

See also the related

• How to calculate a general solution to a linear system from a kernel.

Answer 2

The reason is that if you sum up the first 3 equation then substract the following 3, you get 0=0. The system of equations is therefore not invertible (one of the first six equations is superfluous, so you have 7 equations and 8 variables), hence there can be more than one solution.