# Thread: Simultaneous Equations 4 variables, 4 equations

1. ## Simultaneous Equations 4 variables, 4 equations

Hi,

I have 4 simultaneous equations with 4 variables. I thought that was enough to be able to solve it 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

2. ## Re: Simultaneous Equations 4 variables, 4 equations

Originally Posted by MathFan
Hi,

I have 4 simultaneous equations with 4 variables. I thought that was enough to be able to solve it 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
Unfortunately for you, the four equations are not independent: determinant of &#123;&#123;1, 1, 0, 0&#125;, &#123;0, 0, 1, 1&#125;, &#123;1, 0, 1, 0&#125;, &#123;0, 1, 0, 1&#125;&#125; - Wolfram|Alpha

This means that you don't really have 4 equations with 4 unknowns. Some of the equations can be obtained from the others and so are therefore redundant. Your system does not have a unique solution.

eg.

3. ## Re: Simultaneous Equations 4 variables, 4 equations

Thx for the very quick reply. That's just what I was thinking. However, I've just noticed I missed one equation that might make the difference

a+d = b+c

I'll have another look at it now

4. ## Re: Simultaneous Equations 4 variables, 4 equations

Yes, that leaves it solvable, thx for your help mr fantastic.