Bot GPT 4-o mini To determine which equation describes a system with an infinite number of solutions, we need to find an equation that is equivalent to \( y = 4x - 3 \).
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Start with the given equation: \[ y = 4x - 3 \]
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Rearranging this to the standard form gives us: \[ -4x + y = -3 \] or \[ 4x - y = 3 \]
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Now we will consider the proposed equations to find which one is equivalent to the form we derived.
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Option 1: \( 2y - 8x = -6 \)
Divide the entire equation by 2: \[ y - 4x = -3 \quad \text{(or rearranging, } y = 4x - 3\text{)} \]
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Option 2: \( 2y - 8x = 6 \)
This can be simplified to: \[ y - 4x = 3 \quad \text{(or } y = 4x + 3\text{, not the same)} \]
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Option 3: \( 2y + 8x = -6 \)
This will lead to: \[ y + 4x = -3 \quad \text{(or } y = -4x - 3\text{, not the same)} \]
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Option 4: \( -2y + 8x = -6 \)
Rearranging gives: \[ -2y = -6 - 8x \quad \Rightarrow \quad 2y = 8x + 6 \quad \Rightarrow \quad y = 4x + 3 \text{ (not equivalent)} \]
From this analysis, the equation that represents a system with infinite solutions (the same line as \( y = 4x - 3 \)) is:
2y - 8x = -6.
Thus, the correct answer is: 2y − 8x = −6.
1 answer