To solve the system of equations using the substitution method, we have the following equations:
1) \( 9x - 3y = 12 \)
2) \( y + 6 = 2x \)
Let's start with Equation 2 to express \( y \) in terms of \( x \):
\[
y + 6 = 2x
\]
Now, isolate \( y \):
\[
y = 2x - 6
\]
Next, we will substitute this expression for \( y \) into Equation 1:
\[
9x - 3(2x - 6) = 12
\]
Now, distribute the \(-3\):
\[
9x - 6x + 18 = 12
\]
Combine like terms:
\[
3x + 18 = 12
\]
Now, isolate \( x \) by subtracting 18 from both sides:
\[
3x = 12 - 18
\]
\[
3x = -6
\]
Now divide by 3:
\[
x = -2
\]
Next, substitute \( x = -2 \) back into the expression for \( y \):
\[
y = 2(-2) - 6
\]
\[
y = -4 - 6
\]
\[
y = -10
\]
Thus, the solution to the system of equations is:
\[
(x, y) = (-2, -10)
\]
The final answer is \((-2, -10)\).