Question

Solving Simultaneous Equations Using Substitution Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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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 have the following equations:

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

Step 1: Solve one of the equations for one variable. Let’s solve Equation 1 for \( y \).

Starting with Equation 1:
\[
2x + 2y = 6
\]

Subtract \( 2x \) from both sides:
\[
2y = 6 - 2x
\]

Now, divide by 2:
\[
y = 3 - x \quad \text{(Equation 3)}
\]

Step 2: Substitute Equation 3 into Equation 2.

Now substitute \( y = 3 - x \) into Equation 2:
\[
3x + 2(3 - x) = 9
\]

Distributing \( 2 \):
\[
3x + 6 - 2x = 9
\]

Combine like terms:
\[
x + 6 = 9
\]

Subtract \( 6 \) from both sides:
\[
x = 3
\]

Step 3: Substitute \( x \) back into Equation 3 to find \( y \).

Now substitute \( x = 3 \) into Equation 3:
\[
y = 3 - 3
\]
\[
y = 0
\]

So the solution to the system of equations is:
\[
(x, y) = (3, 0)
\]

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