To use the substitution method to solve the system, we need to solve one of the equations for x or y in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable that we can solve.
Let's solve the first equation for x in terms of y:
x + 4y = -9
x = -4y - 9
Now we substitute this expression for x into the second equation:
2x + 5y = -6
2(-4y - 9) + 5y = -6
Simplifying this expression, we get:
-8y - 18 + 5y = -6
-3y = 12
y = -4
Now we can substitute this value of y into either of the original equations to find x. Let's use the first equation:
x + 4y = -9
x + 4(-4) = -9
x - 16 = -9
x = 7
Therefore, the solution to the system is x = 7, y = -4.
Now let's look at the answer choices and see which one matches the equation we got by substituting x = -4y - 9 into the second equation:
A) 2(4-9)+ 5y-6 = -10 + 5y - 6 = 5y - 16
B) 21-4y-9)+5% -6 = -4y + 6
C) 2x+5(4-9)=-6 = 2x - 25 = -6
D) 2x+5(-4y-9)=-6 = 2x - 20y - 45 = -6
The answer choice that matches our equation is D), 2x + 5(-4y - 9) = -6.