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 9x−3y=12
, y+6=2x
.(1 point)
(
)
Remaining Attempts : 3
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Answer 1

To solve the system of equations using the substitution method, follow these steps:

We have:
1. \( 9x - 3y = 12 \) (Equation 1)
2. \( y + 6 = 2x \) (Equation 2)

### Step 1: Solve one equation for one variable

Let's solve Equation 2 for \( y \):
\[
y + 6 = 2x
\]
Subtract 6 from both sides:
\[
y = 2x - 6
\]

### Step 2: Substitute into the other equation

Now, substitute \( y = 2x - 6 \) into Equation 1:
\[
9x - 3(2x - 6) = 12
\]

### Step 3: Simplify and solve for \( x \)

Distributing \(-3\):
\[
9x - 6x + 18 = 12
\]
Combine like terms:
\[
3x + 18 = 12
\]
Subtract 18 from both sides:
\[
3x = 12 - 18
\]
\[
3x = -6
\]
Divide by 3:
\[
x = -2
\]

### Step 4: Substitute back to find \( y \)

Now substitute \( x = -2 \) back into the equation we derived for \( y \):
\[
y = 2(-2) - 6
\]
\[
y = -4 - 6
\]
\[
y = -10
\]

### Final Solution

The solution to the system of equations is:
\[
(x, y) = (-2, -10)
\]

You can check both equations to ensure that these values satisfy them.