To solve the given system of equations using substitution, let’s proceed step-by-step.

Given equations:

1. $-5y - 10 = x$
2. $x + 9y = -2$

Step 1: Solve one equation for one variable

From the first equation:
$-5y - 10 = x$
We can solve for $x$:
$x = -5y - 10$

Step 2: Substitute $x$ into the second equation

Substitute $x = -5y - 10$ into $x + 9y = -2$:
$(-5y - 10) + 9y = -2$

Step 3: Simplify the equation

Combine like terms:
$-5y + 9y - 10 = -2$ $4y - 10 = -2$

Add 10 to both sides:
$4y = 8$

Divide by 4:
$y = 2$

Step 4: Substitute $y = 2$ back into $x = -5y - 10$

$x = -5(2) - 10$ $x = -10 - 10$ $x = -20$

Final Solution:

$x = -20, \, y = 2$

---

Verification:

Substitute $x = -20$ and $y = 2$ into both original equations to ensure they hold true.

1. For $-5y - 10 = x$:
   $-5(2) - 10 = -20 \quad \text{(True)}$

2. For $x + 9y = -2$:
   $-20 + 9(2) = -2$ $-20 + 18 = -2 \quad \text{(True)}$

The solution is verified.

Final Answer:

$\boxed{x = -20, \, y = 2}$

---

Do you want a detailed explanation of any step? 😊
Here are 5 related questions:

1. Can you explain the substitution method in general?
2. How do you decide which variable to isolate first in substitution?
3. How would the solution change if the second equation were $x + 9y = -3$?
4. What other methods can solve systems of linear equations?
5. Can a system of equations have no solution or infinitely many solutions?

Tip: Always verify your solution by substituting it back into the original equations!