Question

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

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.**