Question
Consider the system of equations shown below to answer questions Question 21 and 22.
{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
{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
Answers
GPT-4o mini
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**.
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**.