Algebra: Finding the Equilibrium

x' goes to:  

a + by = ex

x =  (a + by) / e


y' goes to:  

c + dx = fy
c + d(a + by)/e = fy
c + da/e + dby/e = fy
c + da/e = y ( f - db/e)
ec + da = y (ef - db)

y = (-ec - ad)/(bd - ef)


And therefore,     - bc - fa
	           ----------  = x 
	             bd - ef