Question
Which equation will make the systems equivalent?(1 point)
Responses
−8x−5y=6
negative 8 x minus 5 y is equal to 6
−10x−4y=−6
negative 10 x minus 4 y is equal to negative 6
−10x+4y=6
negative 10 x plus 4 y is equal to 6
8x+5y=6
Answers
GPT-4o mini
To determine which equation will make the systems equivalent, we need to check if any of the given equations can be transformed to be equivalent to the first equation:
\(-8x - 5y = 6\).
1. **Multiply by -1**: Changing the signs will yield \(8x + 5y = -6\).
Now let’s compare the other equations:
- For \(-10x - 4y = -6\): This does not match.
- For \(-10x + 4y = 6\): This does not match either.
- For \(8x + 5y = 6\): This does not match as well.
None of these equations match the transformations from the initial equation.
To check for equivalent systems, we can also check if any of the provided equations can be derived by multiplying the original equation by a constant. The coefficient ratios must be the same.
Let's check the second equation:
- **Check \(-10x - 4y = -6\)**:
- It can be multiplied by \(-1\) giving us \(10x + 4y = 6\), but that doesn't yield anywhere close to our original system without changing signs.
Next, let's check the coefficients of \(x\) and \(y\) from the original equation:
From \( -8x - 5y = 6 \):
To find a fitting equation, let's look at each multiplier possible:
\(-10x - 4y = -6\): Multiplying it won't yield equivalent ratios.
\(-10x + 4y = 6\): Again, will not yield.
**Conclusion:**
None of these equations will constitute an equivalent system to \(-8x-5y=6\). If asked to pick one that approaches equivalency, **none apply directly as equivalents** based on potential transformations utilized. Further analysis of potential mistakes in checking proportionate coefficients might be warranted.
\(-8x - 5y = 6\).
1. **Multiply by -1**: Changing the signs will yield \(8x + 5y = -6\).
Now let’s compare the other equations:
- For \(-10x - 4y = -6\): This does not match.
- For \(-10x + 4y = 6\): This does not match either.
- For \(8x + 5y = 6\): This does not match as well.
None of these equations match the transformations from the initial equation.
To check for equivalent systems, we can also check if any of the provided equations can be derived by multiplying the original equation by a constant. The coefficient ratios must be the same.
Let's check the second equation:
- **Check \(-10x - 4y = -6\)**:
- It can be multiplied by \(-1\) giving us \(10x + 4y = 6\), but that doesn't yield anywhere close to our original system without changing signs.
Next, let's check the coefficients of \(x\) and \(y\) from the original equation:
From \( -8x - 5y = 6 \):
To find a fitting equation, let's look at each multiplier possible:
\(-10x - 4y = -6\): Multiplying it won't yield equivalent ratios.
\(-10x + 4y = 6\): Again, will not yield.
**Conclusion:**
None of these equations will constitute an equivalent system to \(-8x-5y=6\). If asked to pick one that approaches equivalency, **none apply directly as equivalents** based on potential transformations utilized. Further analysis of potential mistakes in checking proportionate coefficients might be warranted.