Final answer:
The correct first step to eliminate a variable in the given system of equations is to add the two equations together, which will cancel out the y variable due to the opposite signs in front of the 3y term in each equation.
Step-by-step explanation:
To eliminate a variable in the system of equations -4x - 3y = -33 and 22x + 3y = -21, you can simply add the two equations together. Since they both have the term 3y and one is positive while the other is negative, adding the equations will cancel out the y variable, leading to an equation with only x.
The first step is thus:
-4x - 3y = -33
+ 22x + 3y = -21
-------------------
18x = -54
This results in a simplified equation where y is eliminated, allowing you to solve for x.
After solving for x, you can substitute this value back into one of the original equations to solve for y.