# simple substitution on equation giving dev a ride…

Im a developer working on some veterinary calculators,

I have found all the required equation substitutions needed for my app, but I left the last one for now and is giving me a bit of a doubt filled mind…

Is a simple two linear equations solved by substitution method,

I have::

AB = CD
E = D-B


I need to find B and D…

Any ideas? Is simple, high school stuff, but I have forgotten a bit

thanks a lot!

-

You have: $AB = CD$ and $E = D-B$.
Divide the first equation by $A$: $B = \frac{CD}{A}$, and substitute into the second.
This yields $E = D - \frac{CD}{A} = D(1-\frac{C}{A})$. Therefore $D = \frac{E}{1-\frac{C}{A}}$.
Finally backsubstitute to get $B = \frac{C}{A}\frac{E}{(1-\frac{C}{A})} = \frac{CE}{A-C}$