Solving Simultaneous Equations: e = ab, f = ac, g = db, h = cd

[fenixtx423]

I am having trouble trying to solve the following equations for the variable a in terms of e, f, g, and h, which are known. I keep ending up cancelling out the a term. Can't we solve for it since there are four variables (a,b,c,d) and four equations? How can I solve for a?

e = ab
f = ac
g = db
h = cd

 

[Ishuda]

I am having trouble trying to solve the following equations for the variable a in terms of e, f, g, and h, which are known. I keep ending up cancelling out the a term. Can't we solve for it since there are four variables (a,b,c,d) and four equations? How can I solve for a?

e = ab
f = ac
g = db
h = cd

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Hint: The 4 equations & 4 variables implies a solution is only (partially) true for a set of linear equations and this is not a set of linear equations. Even were it a set of linear equations, you would be guaranteed a unique solution only under specific conditions. Oh, and there really isn't 4 independent equations anyway. The 'knowns' e, f, g, and h must satisfy a specific relationship if there is going to be a solution. Even then the solution for the variables a, b, c, and d are not unique.

 

[fenixtx423]

Thank you all that helps! I was able set up the equations differently and solve what I needed. Thanks