To solve the system of equations using substitution, we will first substitute the expression for \( x \) from the second equation into the first equation.
The equations are:
- \( x + 2y = -10 \)
- \( x = -4y \)
Now substitute \( x \) from the second equation into the first:
\[ -4y + 2y = -10 \]
Combine like terms:
\[ -2y = -10 \]
Now, divide both sides by -2:
\[ y = 5 \]
Next, substitute \( y = 5 \) back into the second equation to find \( x \):
\[ x = -4(5) = -20 \]
So, we have found the values of \( x \) and \( y \):
\[ x = -20 \quad \text{and} \quad y = 5 \]
The ordered pair that is the solution to the system of equations is:
\[ (-20, 5) \]
Thus, the solution is \( (-20, 5) \).