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!