Given ## a,b,c,d,e,f \in \mathbb {R}, ad - bc \neq 0 ##, if ##(x_1,y_1)## and ##(x_2,y_2)## are pairs of real numbers satisfying:
## ax_1 + by_1 = e, cx_1 + dy_1 =f ##
## ax_2 + by_2 = e, cx_2 + dy_2 = f ##
then ## (x_1,y_1) = (x_2,y_2). ##
Here is my attempt at a proof, I have gotten stuck...