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Question: Balancing Equations Function

Question:Balancing Equations Function

Lime Juice 10 Maple 2017
October 26 2017
1

Hi, 

As an example, I have these 3 equations below and I need to balance them similar to balancing a chemical equation.

Equation 1: E1=A+B+C+D
Equation 2: E2=A-B+C-D
Equation 3: E3=C

So, I am wondering if there are any functions or algorithms that allow me to input such that they will give me a result of 

xE1 ± yE2 ± zE3 = wA

where w,x,y &z are integers and x,y & z can be zero. 

Thanks.
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