To solve the system of linear equations:

\[
y = 6x - 11
\]
\[
-2x - 3y = -7
\]

### Step 1: Substitute \( y = 6x - 11 \) into the second equation.

Given:
\[
-2x - 3y = -7
\]

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

### Step 2: Simplify the equation.

Distribute the \(-3\):
\[
-2x - 18x + 33 = -7
\]

Combine like terms:
\[
-20x + 33 = -7
\]

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

Subtract 33 from both sides:
\[
-20x = -7 - 33
\]
\[
-20x = -40
\]

Divide both sides by \(-20\):
\[
x = 2
\]

### Step 4: Solve for \( y \).

Now substitute \( x = 2 \) back into the first equation:
\[
y = 6(2) - 11
\]
\[
y = 12 - 11
\]
\[
y = 1
\]

### Solution:

The solution to the system of equations is:
\[
x = 2, \quad y = 1
\]

Would you like more details or have any questions about this process?

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Here are 5 follow-up questions related to this problem:

1. What is the graphical interpretation of the solution \( (2, 1) \) for this system of equations?
2. How would you solve this system using the elimination method?
3. Can you solve the system by converting both equations into slope-intercept form?
4. What would happen if both lines were parallel? How would that affect the solution?
5. How can you verify that \( (2, 1) \) is the correct solution?

**Tip:** When solving systems of equations, always double-check by substituting your solutions back into the original equations to verify accuracy.

Learn how to solve a system of linear equations with the equations y = 6x - 11 and -2x - 3y = -7. This problem involves using the substitution method to find the values of x and y. Suitable for Grades 7-9.

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