To solve the system of equations using substitution, we have the following equations:
- \( 2x - 3y = 19 \)
- \( y = x - 7 \)
First, we can substitute \( y \) from the second equation into the first equation:
\[ 2x - 3(x - 7) = 19 \]
Now, distribute \( -3 \):
\[ 2x - 3x + 21 = 19 \]
Combine like terms:
\[ -x + 21 = 19 \]
Now, isolate \( x \) by subtracting 21 from both sides:
\[ -x = 19 - 21 \]
\[ -x = -2 \]
Multiply both sides by -1:
\[ x = 2 \]
Now that we have the value of \( x \), we can substitute this value back into the second equation to find \( y \):
\[ y = x - 7 \]
\[ y = 2 - 7 \]
\[ y = -5 \]
Now we have both values. The solution to the system of equations, represented as an ordered pair \( (x, y) \), is:
\[ \boxed{(2, -5)} \]