# Simultaneous equations, two unknowns

I really should've paid more attention to maths in school...

I have some fairly simple simultaneous equations in the following format.

• VMax = DMax + (DMax - DMin) * GMax
• VMin = DMin - (DMax - DMin) * GMin

Knowns are VMax, VMin, GMax, GMin
Unknowns are DMax, DMin
All values are real numbers

Given the above, how can I re-arrange the equations to solve and determine the values of DMin and DMax?

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First, expand the multiplications:

$VMax=DMax+DMax\cdot GMax-DMin\cdot GMax$

$VMin=DMin-DMax\cdot Gmin+DMin\cdot GMin$

Solve the first equation for DMax

$DMax=\frac {VMax+DMin\cdot GMax}{1+GMax}$

Insert this value in the second equation, leaving you one equation in $DMin$, which you solve the same way. Then insert the value you find for $DMin$ into this one.

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Wow, it seems I'm really thick! I'm working through this now, thanks –  Dr. ABT Aug 5 '12 at 22:24
Slight correction, second expanded equation should be VMin=DMin − DMax⋅Gmin + DMin⋅GMin. I think I've got it though from this - thanks! :) –  Dr. ABT Aug 5 '12 at 22:40
@Dr.ABT: You are right. I fixed the typo –  Ross Millikan Aug 5 '12 at 23:33