Question

Solve the system using substitution method
y = 6x - 11
-2x - 3y = -7

Answer 1

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

1. \( y = 6x - 11 \)
2. \( -2x - 3y = -7 \)

We will substitute \( y \) from the first equation into the second equation.

### Step 1: Substitute \( y \)

Substituting \( y = 6x - 11 \) into the second equation:

\[
-2x - 3(6x - 11) = -7
\]

### Step 2: Simplify the Equation

Now, distribute the \(-3\):

\[
-2x - 18x + 33 = -7
\]

Combine like terms:

\[
-20x + 33 = -7
\]

### Step 3: Solve for \( x \)

Subtract 33 from both sides:

\[
-20x = -7 - 33
\]
\[
-20x = -40
\]

Now, divide both sides by \(-20\):

\[
x = \frac{-40}{-20} = 2
\]

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

Now that we have \( x = 2 \), we substitute it back into the first equation to find \( y \):

\[
y = 6(2) - 11
\]
\[
y = 12 - 11
\]
\[
y = 1
\]

### Step 5: Write the Solution

The solution to the system of equations is:

\[
(x, y) = (2, 1)
\]

**Final Solution: \( (2, 1) \)**