Solving 4 product equations 4 unknowns

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SUMMARY

The discussion focuses on solving a system of four equations with four unknowns, specifically in the form of a1*b1=c1, a2*b1=c2, a1*b2=c3, and a2*b2=c4. The method involves dividing the first two equations to eliminate b1 and the last two to eliminate b2, resulting in two equations that can be solved for a1 and a2. This approach simplifies the problem and allows for a straightforward solution of the unknowns in terms of the known values c1, c2, c3, and c4.

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golmschenk
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I ran into this in my research and I'm certain it should be extremely simple, but for some reason I can seem to remember how to do it. If I have a setup such as:
a1*b1=c1
a2*b1=c2
a1*b2=c3
a2*b2=c4
And the c's are known values, how do I solve for the a's and b's in terms of c's?
 
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Take the first two equations and divide them to eliminate b1

Take the last two and divide them and eliminate b2


You will now have two equations in a1 and a2
 

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