To use the elimination method effectively for the given system of equations:
- \( 6x - 3y = 18 \)
- \( -3x - 9y = -93 \)
We can choose to manipulate one of the equations so that the coefficients of either \(x\) or \(y\) will allow us to eliminate one of the variables when we add or subtract the equations.
Looking at the second equation, it might be useful to multiply it by -1 so it can potentially match the coefficient of the first equation. However, since the coefficients of \(y\) will not directly allow for easy elimination, we can multiply the first equation by a number that makes the coefficients of \(y\) in the first equation match the coefficients in the second equation.
If we multiply the first equation by -3, we get:
\[ -18x + 9y = -54 \]
This leads us to the following new system of equations:
- \(-18x + 9y = -54\)
- \(-3x - 9y = -93\)
Adding both equations will result in eliminating \(y\).
Therefore, the best first action is:
multiply the first equation by -3.