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Let's solve the system of equations using the **substitution method**:

Given:
1. \(x - y = 11\)
2. \(2x + y = 19\)

### Step 1: Solve one equation for one variable in terms of the other
From the first equation \(x - y = 11\), solve for \(x\) in terms of \(y\):
\[
x = y + 11
\]

### Step 2: Substitute the expression for \(x\) in the second equation
Now, substitute \(x = y + 11\) into the second equation \(2x + y = 19\):
\[
2(y + 11) + y = 19
\]

### Step 3: Simplify and solve for \(y\)
Distribute the 2:
\[
2y + 22 + y = 19
\]
Combine like terms:
\[
3y + 22 = 19
\]
Subtract 22 from both sides:
\[
3y = -3
\]
Divide by 3:
\[
y = -1
\]

### Step 4: Substitute \(y = -1\) back into the equation for \(x\)
Now, use \(x = y + 11\) and substitute \(y = -1\):
\[
x = -1 + 11 = 10
\]

### Final Solution
The solution to the system of equations is:
\[
x = 10, \quad y = -1
\]

Would you like further clarifications, or is there another step you'd like me to explore?

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Here are 5 related questions to enhance your understanding:
1. What would happen if we used the elimination method instead of substitution?
2. How can we verify if our solution is correct?
3. Can every system of linear equations be solved using substitution? If not, why?
4. What are other methods to solve systems of equations?
5. How do substitution and elimination methods compare in efficiency for larger systems?

**Tip:** Always substitute your solutions back into the original equations to confirm they satisfy both equations.

Solve using Substitution Method: x - y = 11, 2x + y = 19

Learn how to solve the system of linear equations x - y = 11 and 2x + y = 19 using the substitution method. This step-by-step guide covers key algebraic concepts for students in Grades 8-10.

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