Use the substitution method to solve the system 9x−3y=12

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 \((-2, -10)\).