https://file.aiquickdraw.com/mathbot/file/1727476694429z1cms492.jpg

The image you provided contains a system of equations. Let me write them out clearly:

\[
\text{a. }
\begin{cases}
2x + y = 4 \\
x - y = 11
\end{cases}
\]

The question asks whether "Diego's method" works. To determine this, we would need to solve the system of equations. Let's solve it step-by-step to see if there's any potential issue with the method.

### Step 1: Solve the system
We can use either substitution or elimination. Let's use substitution.

From the second equation:
\[
x - y = 11 \implies x = y + 11
\]

Now, substitute \( x = y + 11 \) into the first equation:
\[
2(y + 11) + y = 4
\]
Expanding:
\[
2y + 22 + y = 4 \implies 3y + 22 = 4
\]
Subtract 22 from both sides:
\[
3y = 4 - 22 = -18
\]
Divide by 3:
\[
y = -6
\]

### Step 2: Find \( x \)
Substitute \( y = -6 \) into \( x = y + 11 \):
\[
x = -6 + 11 = 5
\]

### Step 3: Verify the solution
Substitute \( x = 5 \) and \( y = -6 \) into both original equations to verify:

1. \( 2(5) + (-6) = 10 - 6 = 4 \) ✔
2. \( 5 - (-6) = 5 + 6 = 11 \) ✔

Thus, \( x = 5 \) and \( y = -6 \) is the correct solution.

If Diego used the substitution method correctly as we did here, then his method works. However, if his approach or reasoning differed, it might have led to an incorrect result. Without knowing Diego's exact method, we can only say that this standard method is correct.

Would you like to explore further details or clarify Diego's method?

---

Here are 5 related questions for deeper understanding:
1. How would the solution change if the second equation were \( x + y = 11 \)?
2. What method would be faster: substitution or elimination in this case?
3. How can you check your solution without solving the system again?
4. What happens if you switch the variables in the equations?
5. Can systems of equations always be solved using substitution?

**Tip:** After solving systems of equations, always plug your solution back into the original equations to verify the accuracy.

Does Diego's method work for the system of equations 2x + y = 4 and x - y = 11? Explain your reasoning.

Learn how to solve the system of equations 2x + y = 4 and x - y = 11 using the substitution method. This solution explores algebraic concepts and verifies the solution step-by-step. Suitable for students in Grades 8-10.

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