To solve the system of equations using substitution, we'll first rewrite the equations clearly:
- \( 6x - 4y = 54 \)
- \( -9x + 2y = 69 \)
Let's solve the first equation for \( y \):
\[ 6x - 4y = 54 \]
Rearranging for \( y \):
\[ -4y = 54 - 6x \]
\[ y = \frac{6x - 54}{4} \]
\[ y = \frac{3x - 27}{2} \]
Now that we have \( y \) in terms of \( x \), we can substitute this expression for \( y \) into the second equation:
\[ -9x + 2y = 69 \]
Substituting \( y \):
\[ -9x + 2\left(\frac{3x - 27}{2}\right) = 69 \]
Multiply by 2 to eliminate the fraction:
\[ -9x + (3x - 27) = 69 \]
Combine like terms:
\[ -6x - 27 = 69 \]
Now, add 27 to both sides:
\[ -6x = 69 + 27 \]
\[ -6x = 96 \]
Divide by -6:
\[ x = -16 \]
Now, substitute \( x = -16 \) back into the expression we found for \( y \):
\[ y = \frac{3(-16) - 27}{2} \]
\[ y = \frac{-48 - 27}{2} \]
\[ y = \frac{-75}{2} \]
\[ y = -37.5 \]
Thus, the solution to the system of equations is:
\[ x = -16, \quad y = -37.5 \]
So the final answer is:
\[ \boxed{(-16, -37.5)} \]