I have two operations too chose from. Each operation is essentially a base added too a coefficient and a variable.

Since each operation appears to be linear and the two operations exist within the same system I decided to determine were the lines intercept.

This is not a problem out of a math book.

(500+.2142y)(2.06x)+(500+.2142y)(1-x)+(500+.6y)(2.06x)+(500+.6y)(1-x)

And

(872+.3858y)(1-x)+(872+.3858y)(2.06x)

Since I want to find the point where x and y are equal to each other I set the two as equal to each other. After Reducing and simplifying I get;

1.180548yx+924.32x+.3858y+872=.86305yx+1414.04x+.8 142y+1334

I decided it would be quicker to work the problem out with out all the long coefficients too see if I could get at a solution at all. For simplicities sake I've been writing it out on paper as;

xy+x+y+10=3xy+2x+3y+7

There are no fractions so I start by factoring.

x(y+1)+y+10=x(3y+2)3y+7

Then move terms over

x(y+1)+y-3y+10-7=x(3y+2)

Combine like terms

x(y+1)-2y+3=x(3y+2)

This is were i get stuck. If I divide away the 3y+2 on the right hand side and move it too the left, I still have an x sitting over on the left side.

Or;

x(y+1)-2y+3/(3y+2)=x

I can't just divide out the x on the left, since that would leave me with a 1 on the other side, X/X.

At first I thought it was a no solution type problem, but that doesn't seem to make sense. Have I just set the whole thing up wrong?