https://file.aiquickdraw.com/mathbot/file/1726844733477jxfikynx.jpg

The system of equations is:

\[
-4x - y = 6
\]
\[
y = 2x
\]

We are instructed to solve this system by substitution. Let's follow these steps:

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

Substitute \( y = 2x \) into the first equation:
\[
-4x - (2x) = 6
\]

### Step 2: Solve for \( x \)

Simplify the equation:
\[
-4x - 2x = 6
\]
\[
-6x = 6
\]
Now, solve for \( x \) by dividing both sides by -6:
\[
x = -1
\]

### Step 3: Solve for \( y \)

Now that we have \( x = -1 \), substitute this value into the equation \( y = 2x \) to find \( y \):
\[
y = 2(-1) = -2
\]

### Solution:

The solution to the system is:
\[
x = -1, \quad y = -2
\]

You can submit \((-1, -2)\) as the solution.

Do you want more details or have any questions?  
Here are five related questions to expand your understanding:

1. How would you solve this system graphically?
2. Can this system be solved using elimination? How?
3. What does it mean for a system to have no solution?
4. What if the system had an infinite number of solutions—how would we identify that?
5. How can we check that the solution \( (-1, -2) \) is correct?

**Tip:** Always substitute your values back into the original equations to check the solution!

Solve the system by substitution: -4x - y = 6 and y = 2x

Learn how to solve a system of equations by substitution, using the example -4x - y = 6 and y = 2x. This step-by-step guide explains how to find the values of x and y, perfect for students in Grades 8-10.

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