To solve the system of equations using elimination, the goal is to create coefficients for either \(x\) or \(y\) that are equal (so they can be eliminated when added or subtracted).
The equations are: \[ \text{i. } 2x + y = -3 \] \[ \text{ii. } 3x - 2y = 2 \]
One effective way to start would be to eliminate \(y\).
To eliminate \(y\), you can multiply equation i by \(2\) to match the \(y\) coefficient of equation ii. This way, you can set up a situation where adding the two equations will eliminate \(y\).
Thus, the best way to begin is: Multiply equation i by 2 and multiply equation ii by 1 (no change needed for ii).
However, since that option is not available in your responses, we have to choose another option among the given ones.
Looking at the options provided:
- Multiply equation i by 2 and multiply equation ii by 3
- Multiply equation ii by 2
- Multiply equation i by 2
- Multiply equation ii by 2 and multiply equation i by -2
The first option (Multiply equation i by 2 and multiply equation ii by 3) gives us:
- From equation i: \(2(2x+y) = 2(-3) \Rightarrow 4x + 2y = -6\)
- From equation ii: \(3(3x-2y) = 3(2) \Rightarrow 9x - 6y = 6\)
This will allow for elimination of \(y\) by manipulating the coefficients correctly afterward.
Therefore, the best answer is: Multiply equation i by 2 and multiply equation ii by 3.