Simultaneous Equations 4 variables, 4 equations

[MathFan]

Hi,


I have 4 simultaneous equations with 4 variables. I thought if there were at least the same amount of equations as variables it should be solvable but I can't figure it out (or else, why it can't be figured out)




a + b = 4903716584 (1)
c + d = 4316123816 (2)
c + a = 3628610024 (3)
d + b = 5591230376 (4)


From these I went this way


(1)-(3) b - c = 4903716584 - 3628610024 = 1275106560
(1)-(4) a - d = 4903716584 - 5591230376 = -687513792
(2)-(3) gives -((1)-(4))
(2)-(4) gives -((1)-(3))


that doesn't seem a lot of help. I am not able to isolate any single variable.
Can someone help please ?


thx

 

[MathFan]

Try it this way:

\(\displaystyle a = 4903716584 - b.\)

Now you can restate equation 3 in terms of c and b. You are now down to three equations in three unknowns.

Thx for the quick reply JeffM, I have also tried that with this result

a = 4903716584 - b


c + d = 4316123816 (2)
c - b = -1275106560 (3)
d + b = 5591230376 (4)


c = 4316123816 - d


- d - b = -5591230376 (3)
d + b = 5591230376 (4)


Maybe I have one of the unsolvable ones then?

 

[MathFan]

blast, just realised I missed one other equation

a+d = b+c

and this does lead to a single answer.

Thx again