To use the substitution method to solve the system of equations \( 2x + 2y = 6 \) and \( 3x + 2y = 9 \), we'll follow these steps:
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Solve one equation for one variable. Let's solve the first equation for \( y \):
\[ 2x + 2y = 6 \]
Rearranging gives:
\[ 2y = 6 - 2x \]
Dividing by 2:
\[ y = 3 - x \]
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Substitute into the other equation. Now, we can substitute \( y \) into the second equation \( 3x + 2y = 9 \):
\[ 3x + 2(3 - x) = 9 \]
Simplifying that:
\[ 3x + 6 - 2x = 9 \]
This simplifies to:
\[ x + 6 = 9 \]
Subtracting 6 from both sides gives:
\[ x = 3 \]
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Substitute back to find \( y \). Now, substitute \( x = 3 \) back into the expression we found for \( y \):
\[ y = 3 - x \]
Substituting \( x = 3 \) gives:
\[ y = 3 - 3 = 0 \]
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Write the solution. The solution to the system of equations is:
\[ (x, y) = (3, 0) \]
Thus, the final answer is \( (3, 0) \).