We can solve this system of equations by substitution method.
Starting with the first equation: x + 4y = 0
Solving for x: x = -4y
Next, substitute this expression for x in the second equation:
2x - y = 18
2(-4y) - y = 18
-8y - y = 18
-9y = 18
Solving for y: y = 2
Finally, substitute this expression for y back into the expression for x:
x = -4y
x = -4(2)
x = -8
So, the solution to the system of equations is (x, y) = (-8, 2).