Question

Question
Use the substitution method to solve the system 2x+2y=6
, 3x+2y=9
.(1 point)
(
)

Answer 1

To use the substitution method to solve the system of equations \( 2x + 2y = 6 \) and \( 3x + 2y = 9 \), we'll follow these steps:

1. **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:

\[
y = 3 - x
\]

2. **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:

\[
x = 3
\]

3. **Substitute back to find \( y \)**. Now, substitute \( x = 3 \) back into the expression we found for \( y \):

\[
y = 3 - x
\]

Substituting \( x = 3 \) gives:

\[
y = 3 - 3 = 0
\]

4. **Write the solution**. The solution to the system of equations is:

\[
(x, y) = (3, 0)
\]

Thus, the final answer is \( (3, 0) \).