To eliminate one of the variables from the system of equations:
i. \( 2x + y = -3 \)
ii. \( 3x - 2y = 2 \)
The best way to begin is to make the coefficients of \( y \) the same in both equations.
From equation i, we have \( y \) as it is, which has a coefficient of 1. We can multiply equation i by 2 to match the coefficient of \( y \) in equation ii, which is -2.
So, multiplying equation i by 2 will give us:
- \( 4x + 2y = -6 \) (after multiplying equation i by 2)
Now, equation ii already has the necessary coefficient (-2) for \( y \) to allow for elimination when we set up to subtract or add the equations.
In this case, the best choice to begin is:
Multiply equation i by 2 and multiply equation ii by -1, which is equivalent to multiplying equation i by 2 and keeping equation ii as is or vice versa.
However, from the provided answer options, the most straightforward choice to prepare for elimination is:
Multiply equation i by 2.
This allows you to set it up efficiently for elimination.
Thus, the response would be:
Multiply equation i by 2.