To solve the system of equations:
- \( x - y = 4 \)
- \( 3x - 3y = -6 \)
Let's start with the first equation:
From \( x - y = 4 \), we can express \( x \) in terms of \( y \):
\[ x = y + 4 \]
Now, substitute this expression for \( x \) into the second equation:
\[ 3(y + 4) - 3y = -6 \]
Distributing the 3 gives us:
\[ 3y + 12 - 3y = -6 \]
Now the \( 3y \) terms cancel out:
\[ 12 = -6 \]
This statement is false, which indicates that the system of equations is inconsistent. Therefore, there is no solution to this system of equations. The lines represented by these equations are parallel and will never intersect.