Question

Solve the system using substitution method
x + 3y = 6
2x + 8y = -12

Answer 1

To solve the system of equations using the substitution method, we'll start with the given equations:

1. \( x + 3y = 6 \) (Equation 1)
2. \( 2x + 8y = -12 \) (Equation 2)

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

Let's solve Equation 1 for \( x \):

\[
x = 6 - 3y
\]

### Step 2: Substitute into the other equation

Now, substitute \( x = 6 - 3y \) into Equation 2:

\[
2(6 - 3y) + 8y = -12
\]

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

Now simplify the equation:

\[
12 - 6y + 8y = -12
\]

Combine like terms:

\[
12 + 2y = -12
\]

Subtract 12 from both sides:

\[
2y = -12 - 12
\]

\[
2y = -24
\]

Now, divide by 2:

\[
y = -12
\]

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

Next, substitute \( y = -12 \) back into the equation for \( x \):

\[
x = 6 - 3(-12)
\]

\[
x = 6 + 36
\]

\[
x = 42
\]

### Step 5: Summarize the solution

The solution to the system of equations is:

\[
x = 42, \quad y = -12
\]

Thus, the solution to the system is \( (42, -12) \).