Question

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

Answer 1

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

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

**Step 1: Solve one of the equations for one variable.**

Let's solve the first equation for \(y\):

\[
2x + 2y = 6
\]

First, 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:

\[
3x + 2y = 9
\]

Substituting for \(y\):

\[
3x + 2(3 - x) = 9
\]

**Step 3: Simplify and solve for \(x\).**

Now simplify the equation:

\[
3x + 6 - 2x = 9
\]

Combine like terms:

\[
x + 6 = 9
\]

Now, subtract 6 from both sides:

\[
x = 3
\]

**Step 4: Substitute back to find \(y\).**

Now that we have \(x = 3\), we can substitute back to find \(y\):

\[
y = 3 - x = 3 - 3 = 0
\]

**Step 5: Write the solution.**

The solution to the system of equations is:

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

**Final Answer: \( (3, 0) \)**