To solve the system of equations using the substitution method, we start with the two equations provided:
- \( 2x + 2y = 6 \)
- \( 3x + 2y = 9 \)
Step 1: Solve one equation for one variable.
Let's solve the first equation for \( y \):
\[ 2x + 2y = 6 \]
Subtract \( 2x \) from both sides:
\[ 2y = 6 - 2x \]
Now, divide by 2:
\[ y = 3 - x \]
Step 2: Substitute this expression for \( y \) into the second equation.
Now we substitute \( y = 3 - x \) into the second equation \( 3x + 2y = 9 \):
\[ 3x + 2(3 - x) = 9 \]
Distribute \( 2 \):
\[ 3x + 6 - 2x = 9 \]
Step 3: Simplify and solve for \( x \).
Combine like terms:
\[ (3x - 2x) + 6 = 9 \]
This simplifies to:
\[ x + 6 = 9 \]
Now, subtract \( 6 \) from both sides:
\[ x = 3 \]
Step 4: Substitute \( x \) back to find \( y \).
Now that we have \( x \), we can substitute it back into the equation \( y = 3 - x \):
\[ y = 3 - 3 = 0 \]
Step 5: Write the solution as an ordered pair.
The solution to the system of equations is:
\[ (x, y) = (3, 0) \]
So the final answer is:
\[ (3, 0) \]