Answer
No solutions.
The lines are parallel to each other.
Work Step by Step
We need to solve the given system of equations:
$$5x-5y-3=0 ~~~(1) \\ x-y-12=0 ~~~(2)$$
Write each equation in the standard form to obtain the equivalent system:
$$5x-5y=3 ~~~(3) \\ x-y=12 ~~~(4)$$
Multiply the second equation by $-5$ to obtain the equivalent equation:
$$-5x+5y=-60 ~~~~(5)$$
Add equations $(3)$ and $(5)$ to obtain:
$$(5x-5y)+(-5x+5y)=3+(-60) \\ 0= -57 $$
Both variables were eliminated and resulted in a false statement/equation.
This means that the system of equations is inconsistent and has no solutions.
This means that the lines are parallel.
