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To solve this problem, we need to find the values of \( a \) and \( b \) that satisfy both given equations:

1. \( 3a + 4b = 11 \)
2. \( b = 2a \)

### Step 1: Substitute \( b = 2a \) into the first equation.
Replace \( b \) in the first equation with \( 2a \):

\[
3a + 4(2a) = 11
\]

\[
3a + 8a = 11
\]

\[
11a = 11
\]

### Step 2: Solve for \( a \).
Divide both sides by 11:

\[
a = 1
\]

### Step 3: Find \( b \) using \( b = 2a \).
Substitute \( a = 1 \) into \( b = 2a \):

\[
b = 2(1) = 2
\]

### Step 4: Add the values of \( a \) and \( b \) together.
\[
a + b = 1 + 2 = 3
\]

The correct answer is **A. 3**.

Do you want more details or have any questions? Here are some related questions you might consider:

1. How can you solve systems of equations using substitution?
2. What other methods exist for solving systems of linear equations?
3. Can you solve systems with more than two variables?
4. What are the conditions for a system of equations to have a unique solution?
5. How does graphing help in visualizing the solutions of linear equations?

**Tip:** Always check your solutions by substituting them back into the original equations to ensure they satisfy both equations.

Find the values for a and b that satisfy both of the following equations. Add the values found together to get one number: 3a + 4b = 11, b = 2a

Learn how to solve the linear system of equations 3a + 4b = 11 and b = 2a using substitution. This step-by-step solution covers key algebraic concepts. Suitable for students in Grades 7-9.

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