We can use substitution to solve this system of equations. We will solve for y in one of the equations and then substitute that expression for y in the other equation. Here's how:
From the first equation, we can solve for y to get y = 4x + 6.
Now we can substitute 4x + 6 for y in the second equation and solve for x:
-5x - (4x + 6) = 21
-5x - 4x - 6 = 21
-9x = 27
x = -3
Now that we have x, we can substitute -3 back into one of the equations and solve for y:
-4(-3) + y = 6
12 + y = 6
y = -6
Therefore, the solution to the system of equations is x = -3 and y = -6.