Let's solve the given system of equations:

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

Step 1: Substitution

Since we know that $x = -2y$ from the second equation, we can substitute this into the first equation.

Substitute $-2y$ for $x$ in the first equation:

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

Step 2: Simplify the equation

Now, simplify the equation:

$14y - 10y = 40$

$4y = 40$

Step 3: Solve for $y$

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

Step 4: Solve for $x$

Now, use the second equation to find $x$:

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

Solution:

The solution to the system of equations is: $x = -20, \quad y = 10$

Would you like further details or have any questions?

Related questions:

1. How do you solve systems of equations using substitution?
2. What is the method of elimination in solving systems of equations?
3. How can graphing help in solving systems of equations?
4. What are consistent and inconsistent systems of equations?
5. What happens when you have a system of equations with no solution?

Tip: When solving systems of equations, always try to simplify terms as much as possible before solving to avoid errors.