Julie is asked to solve the system below by elimination. Which of the following steps would be the best way to begin?

Question

i. 2x+y=−3


ii. 3x−2y=2


(1 point)
Responses

Multiply equation i by 2 and multiply equation ii by 3
Multiply equation i by 2 and multiply equation ii by 3

Multiply equation ii by 2
Multiply equation ii by 2

Multiply equation i by 2
Multiply equation i by 2

Multiply equation ii by 2 and multiply equation i by -2

Answer 1

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:

1. $4x+2y=-6$ (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.