I have a system of three equations:
$$a_1- (b_1x+cx^2-cx) + (dx - x^2 + x) - yz = 0 $$ $$a_2- (b_2x+cx^2-cx) + (dx - x^2 + x) - (y+1)z = 0 $$ $$a_3- (b_3x+cx^2-cx) + (dx - x^2 + x) - (y+2)z = 0 $$
All coefficients $a,b,c,d$ are given (real numbers). The variables are $x,y,z$.
Does this system make sense and if so, how can it be solved over real numbers?
Hint
Subract the first from the second : $y$ disappears; subract the second from the third and no more $y$.
So, you are left with two linear equations in $x$ and $z$; solve them (it is simple).
When you have the solution, use the first to get $y$.