Question
You are given the system of equations :
16x−10y=10
−8x−6y=6
To solve this by elimination, which of the following is one possible first step you could take?
(1 point)
Responses
(8,−1)
open paren 8 comma negative 1 close paren
Multiply both equations by -2 to eliminate the y
Multiply both equations by -2 to eliminate the y
(0,−2)
open paren 0 comma negative 2 close paren
There is no solution.
There is no solution.
Add the equations together.
Add the equations together.
(0,−1)
open paren 0 comma negative 1 close paren
Multiply the second equation by 2 to help eliminate the x.
Multiply the second equation by 2 to help eliminate the x.
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16x−10y=10
−8x−6y=6
To solve this by elimination, which of the following is one possible first step you could take?
(1 point)
Responses
(8,−1)
open paren 8 comma negative 1 close paren
Multiply both equations by -2 to eliminate the y
Multiply both equations by -2 to eliminate the y
(0,−2)
open paren 0 comma negative 2 close paren
There is no solution.
There is no solution.
Add the equations together.
Add the equations together.
(0,−1)
open paren 0 comma negative 1 close paren
Multiply the second equation by 2 to help eliminate the x.
Multiply the second equation by 2 to help eliminate the x.
Skip to navigation
Answers
Answered by
GPT-4o mini
To solve the given system of equations using the elimination method, let’s rewrite the equations for clarity:
1) \( 16x - 10y = 10 \)
2) \( -8x - 6y = 6 \)
Looking at the options provided, we want to take a step that would help eliminate one of the variables when we add or subtract the equations.
### Analyzing the options:
1. **Multiply both equations by -2 to eliminate the y**:
This would change the first equation to \( -32x + 20y = -20 \) and the second to \( 16x + 12y = -12 \). This step does not directly eliminate y, so it may not be the best first step.
2. **There is no solution**:
This option does not require action but determines the nature of the equations. We should investigate whether the system is consistent or inconsistent by looking for solutions first.
3. **Add the equations together**:
Adding the two equations does not instantly help with elimination as we can see that both equations have different coefficients for x and y.
4. **Multiply the second equation by 2 to help eliminate the x**:
This would change the second equation to \( -16x - 12y = 12 \). This matches the coefficient of \( x \) from the first equation when added, which could help eliminate x.
### Conclusion:
The best first step is **"Multiply the second equation by 2 to help eliminate the x."** This will allow the \( x \) terms to cancel each other out when you proceed with elimination.
1) \( 16x - 10y = 10 \)
2) \( -8x - 6y = 6 \)
Looking at the options provided, we want to take a step that would help eliminate one of the variables when we add or subtract the equations.
### Analyzing the options:
1. **Multiply both equations by -2 to eliminate the y**:
This would change the first equation to \( -32x + 20y = -20 \) and the second to \( 16x + 12y = -12 \). This step does not directly eliminate y, so it may not be the best first step.
2. **There is no solution**:
This option does not require action but determines the nature of the equations. We should investigate whether the system is consistent or inconsistent by looking for solutions first.
3. **Add the equations together**:
Adding the two equations does not instantly help with elimination as we can see that both equations have different coefficients for x and y.
4. **Multiply the second equation by 2 to help eliminate the x**:
This would change the second equation to \( -16x - 12y = 12 \). This matches the coefficient of \( x \) from the first equation when added, which could help eliminate x.
### Conclusion:
The best first step is **"Multiply the second equation by 2 to help eliminate the x."** This will allow the \( x \) terms to cancel each other out when you proceed with elimination.
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