Question
Solving Simultaneous Equations Using Substitution Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items
Question
Use the substitution method to solve the system 2x+2y=6
, 3x+2y=9
.(1 point)
(
)
Answers
GPT-4o mini
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 \( (3, 0) \).
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 \( (3, 0) \).