Solve the system by substitution.

-10y = x
-5x - 7y = 43

We can start by solving the first equation for x:

x = -10y.

Then we substitute this expression for x in the second equation:

-5(-10y) - 7y = 43.

Simplifying this equation gives:

50y - 7y = 43.

Combining like terms gives:

43y = 43.

Dividing both sides by 43 gives:

y = 1.

Now we can substitute this value back into the first equation to solve for x:

x = -10(1) = -10.

Therefore, the solution to the system of equations is x = -10 and y = 1.