Question

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

Answer 1

To solve the system of equations using the substitution method, we start with the two equations provided:

1. \( 2x + 2y = 6 \)
2. \( 3x + 2y = 9 \)

**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:

\[
(3, 0)
\]