To determine which pairs of equations have exactly the same solution, we need to solve each pair of equations.
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First Pair:
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\(-3.2x = 0.64\)
- Solving for \(x\): \[ x = \frac{0.64}{-3.2} = -0.2 \]
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\( \frac{x}{4} = -0.05\)
- Solving for \(x\): \[ x = -0.05 \times 4 = -0.2 \]
Both equations have the solution \(x = -0.2\).
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Second Pair:
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\(\frac{x}{3.2} = 1.8\)
- Solving for \(x\): \[ x = 1.8 \times 3.2 = 5.76 \]
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\(1.8x = 3.2\)
- Solving for \(x\): \[ x = \frac{3.2}{1.8} \approx 1.777... \]
These two equations do not have the same solution.
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Third Pair:
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\(\frac{3}{8}x = 1\)
- Solving for \(x\): \[ x = 1 \times \frac{8}{3} = \frac{8}{3} \]
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\(13x = 18\)
- Solving for \(x\): \[ x = \frac{18}{13} \]
These two equations do not have the same solution.
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Fourth Pair:
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\(-\frac{3}{4}x = \frac{5}{2}\)
- Solving for \(x\): \[ x = \frac{5/2}{-3/4} = \frac{5 \cdot 4}{2 \cdot -3} = \frac{20}{-6} = -\frac{10}{3} \]
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\(\frac{5}{2}x = -\frac{3}{4}\)
- Solving for \(x\): \[ x = \frac{-3/4}{5/2} = -\frac{3 \cdot 2}{4 \cdot 5} = -\frac{6}{20} = -\frac{3}{10} \]
These two equations also do not have the same solution.
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From the analysis above:
The correct answer is the first pair of equations:
- \(-3.2x = 0.64\) and \(\frac{x}{4} = -0.05\) both have the solution \(x = -0.2\).
1 answer