https://file.aiquickdraw.com/mathbot/file/1733670671245p4ntl1hg.jpg

The given system of equations is:

\[
\begin{cases} 
-2x - 3y = -7 \\
y = 6x - 11 
\end{cases}
\]

### Step 1: Substitute \(y = 6x - 11\) into the first equation.
Substitute \(y = 6x - 11\) into \(-2x - 3y = -7\):

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

Expand and simplify:

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

Combine like terms:

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

Solve for \(x\):

\[
-20x = -7 - 33
\]
\[
-20x = -40
\]
\[
x = 2
\]

### Step 2: Solve for \(y\).
Substitute \(x = 2\) into \(y = 6x - 11\):

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

### Final Solution:
The solution to the system of equations is:
\[
(x, y) = (2, 1)
\]

Would you like me to provide a graph or verify the solution? 

### Questions for Deeper Understanding:
1. What method was used to solve the system of equations?
2. Could elimination or graphing also solve this system effectively?
3. What happens if the equations were parallel (no solution)?
4. How do you check if \((2, 1)\) satisfies both equations?
5. How can systems of equations model real-world problems?

### Tip:
Always substitute your solution back into the original equations to verify correctness.

Solve the system of equations: -2x - 3y = -7 and y = 6x - 11.

Learn how to solve the system of equations -2x - 3y = -7 and y = 6x - 11 using the substitution method. This step-by-step solution demonstrates the process and provides verification of the solution. Suitable for students in Grades 8-10.

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