Consider the system of equations shown below to answer questions Question 21 and 22.

Question

{6x-3y=18
-3x-9y=-93

Question 21
In order to solve this system of equations using the elimination/combination method, the first thing Emma should do is
*
0/1
A. multiply the first equation by 3

B. multiply the first equation by -2
C. multiply the second equation by 2
D. multiply the second equation by -3

Answer 1

To solve the system of equations

1. \( 6x - 3y = 18 \)
2. \( -3x - 9y = -93 \)

using the elimination/combination method, Emma should aim to eliminate one of the variables. Let's analyze the equations:

The first equation can be simplified by dividing everything by 3:

1. \( 2x - y = 6 \) (let's call this Equation 1)

Now, for the second equation, if we multiply it by 1 (keeping it the same), we have:

2. \( -3x - 9y = -93 \)

To simplify the second equation, we can divide everything by -3:

2. \( x + 3y = 31 \) (let's call this Equation 2)

Now we have the system of equations:

1. \( 2x - y = 6 \)
2. \( x + 3y = 31 \)

To eliminate one variable, let's consider the possibilities listed in the options:

A. Multiply the first by 3: This would give \( 18x - 9y = 54 \). B. Multiply the first by -2: This would give \( -12x + 6y = -12 \). C. Multiply the second by 2: This would give \( 2x + 6y = 62 \). D. Multiply the second by -3: This would give \( 9x + 27y = 279 \).

Among these options, multiplying the first equation by -2 (Option B) or the second equation by -3 (Option D) would allow us to cancel terms when we add the two equations together. However, multiplying the first equation by -2 is a useful approach because it will directly align the coefficients for elimination with \( y \) terms.

Therefore, the best choice to enable elimination directly would be:

B. multiply the first equation by -2.