How to solve these simultaneous equations:

Question

$1 = 1/2y - bx,$ $1 = 1/2x - ay$

I need x,y it in terms of constants, but I can't figure it out!

Answer 1

From the 1st equation, $2+2bx = y$ Putting in the 2nd, $$1 = \frac12x - 2a-2abx\Leftrightarrow x=\frac{1+2a}{1/2-2ab}$$ if $ab\neq \frac14$. We also have $$y=2+\frac{1+2a}{1-4ab}$$ If $ab=\frac{1}{4}$, $$1 = \frac12x - 2a-2x=-\frac{1}{2}$$ which is impossible