Question

How many solutions are in -x-y=3 and y=x-3

Answer 1

See, pls, offered explanation:
1) the both equations are linear function, it means system made up of the both equation has the only solution.
2) if to prove this:
$\left \{ {{-x-y=3} \atop {-x+y=-3}} \right. \left \{ {{x=0} \atop {y=-3}} \right.$
Answer: one solution.