solve by elimination process 7x-y=27 and -7x+y=-27
These two equations are identical.
They are simple multiples of each other (in this case by -1)
You really only have the one equation, viz. 7x - y = 27
As such, there are an infinite number of solutions.
Or, you could consider it a Diophantine equation with solutions only in the positive single-digit range. In which case, the solution is,
x = 4, y = 1