To solve the system of equations using substitution, we are given the following two equations:

1. $-7x - 10y = 40$
2. $x = -2y$

Step 1: Substitute $x = -2y$ into the first equation

Since $x = -2y$, substitute this expression for $x$ in the first equation.

$-7(-2y) - 10y = 40$

Step 2: Simplify the equation

$14y - 10y = 40$

Combine like terms:

$4y = 40$

Step 3: Solve for $y$

Now divide both sides by 4:

$y = \frac{40}{4} = 10$

Step 4: Solve for $x$

Now that we know $y = 10$, substitute this value back into the equation $x = -2y$:

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

Solution

The solution to the system of equations is:

$x = -20, \quad y = 10$

Would you like more details or have any questions? Here are five related questions you might explore:

1. How can you check the solution of a system of equations?
2. What happens if you graph the system of equations on a coordinate plane?
3. Can a system of equations have no solution or infinitely many solutions? When does that happen?
4. How would the solution change if the second equation was $x = 2y$ instead of $x = -2y$?
5. What are some other methods to solve systems of equations besides substitution?

Tip: When solving by substitution, always simplify equations as much as possible before substituting values for easier calculations.