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 will first solve one of the equations for one variable and then substitute that expression into the other equation.

We have the following system of equations:

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

Let's start with the first equation:

\[
2x + 2y = 6
\]

We can simplify this by dividing every term by 2:

\[
x + y = 3
\]

Now, we can solve for \( y \):

\[
y = 3 - x
\]

Next, we will substitute this expression for \( y \) into the second equation:

\[
3x + 2y = 9
\]

Substituting \( y = 3 - x \):

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

Distributing the 2:

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

Combining like terms:

\[
x + 6 = 9
\]

Now, subtract 6 from both sides:

\[
x = 3
\]

Now that we have the value of \( x \), we can substitute it back into the equation \( y = 3 - x \) to find \( y \):

\[
y = 3 - 3 = 0
\]

Thus, the solution to the system of equations is:

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

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