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.