To solve the system of equations using the substitution method, we first take one equation and solve for one variable in terms of the other.
We have the following system:
- \( 2x + 2y = 6 \)
- \( 3x + 2y = 9 \)
Let's start with the first equation and solve for \( y \):
- Rearrange the first equation:
\[ 2y = 6 - 2x \]
- Divide by 2:
\[ y = 3 - x \]
Now we have expressed \( y \) in terms of \( x \). Next, we substitute this expression for \( y \) into the second equation:
- Substitute \( y = 3 - x \) into the second equation \( 3x + 2y = 9 \):
\[ 3x + 2(3 - x) = 9 \]
- Distribute the 2:
\[ 3x + 6 - 2x = 9 \]
- Combine like terms:
\[ x + 6 = 9 \]
- Subtract 6 from both sides:
\[ x = 3 \]
Now that we have \( x = 3 \), we can substitute this value back into the expression for \( y \):
\[ y = 3 - x = 3 - 3 = 0 \]
So, the solution to the system of equations is:
\[ x = 3, \quad y = 0 \]
Thus, the solution (in ordered pair form) is:
\[ \boxed{(3, 0)} \]