\begin{aligned}
& -4x+11y = 15
\\\\
& x=2y
\end{aligned}

We are given a system of two equations:

\[
1) \ -4x + 11y = 15
\]
\[
2) \ x = 2y
\]

We can solve this system using substitution, as the second equation already expresses \(x\) in terms of \(y\).

### Step 1: Substituting \(x = 2y\) into the first equation
Substitute \(x = 2y\) into the first equation:

\[
-4(2y) + 11y = 15
\]

This simplifies to:

\[
-8y + 11y = 15
\]

\[
3y = 15
\]

### Step 2: Solving for \(y\)

Divide both sides by 3:

\[
y = 5
\]

### Step 3: Solving for \(x\)

Now that we have \(y = 5\), substitute this value into the second equation \(x = 2y\):

\[
x = 2(5) = 10
\]

### Final Answer:
The solution to the system of equations is:

\[
x = 10, \quad y = 5
\]

Would you like any further details or have any questions?

Here are 5 related questions you might want to explore:
1. What is the graphical interpretation of the solution to this system?
2. How can we verify if the solution satisfies both equations?
3. How do you solve systems of equations using the elimination method?
4. What happens if the system has no solution or infinite solutions?
5. How does substitution compare to other methods for solving systems of equations?

**Tip:** When using substitution, always simplify the substituted equation before solving to avoid mistakes.

Learn how to solve the system of linear equations -4x + 11y = 15 and x = 2y using the substitution method. This step-by-step guide walks you through solving for x and y, and understanding key algebraic concepts like substitution. Ideal for students in Grades 8-10.

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