To determine which pair of linear equations has the same solution set, we need to simplify each set of equations and see if they ultimately represent the same line or equality.
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First Pair:
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Equation 1: \( 2(3g + 5) - 2g = 2(4 - g) \)
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Simplifying: \[ 6g + 10 - 2g = 8 - 2g \implies 4g + 10 = 8 - 2g \implies 6g = -2 \implies g = -\frac{1}{3} \]
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Equation 2: \( -36h/6 = 2 \)
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Simplifying: \[ -6h = 2 \implies h = -\frac{1}{3} \]
They have the same solution.
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Second Pair:
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Equation 1: \( 4 = \frac{k}{2} + 5 \)
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Simplifying: \[ \frac{k}{2} = -1 \implies k = -2 \]
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Equation 2: \( \frac{4j - 14}{3} + 5 = 3 \)
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Simplifying: \[ \frac{4j - 14}{3} = -2 \implies 4j - 14 = -6 \implies 4j = 8 \implies j = 2 \]
They do not have the same solution.
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Third Pair:
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Equation 1: \( 3(m + 1) = 10 \)
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Simplifying: \[ 3m + 3 = 10 \implies 3m = 7 \implies m = \frac{7}{3} \]
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Equation 2: \( 6n + 3 = 6 - n \)
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Simplifying: \[ 7n + 3 = 6 \implies 7n = 3 \implies n = \frac{3}{7} \]
They do not have the same solution.
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Fourth Pair:
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Equation 1: \( 4k - 5 = 2k \)
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Simplifying: \[ 4k - 2k = 5 \implies 2k = 5 \implies k = \frac{5}{2} \]
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Equation 2: \( 8j - 2 = 3j \)
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Simplifying: \[ 8j - 3j = 2 \implies 5j = 2 \implies j = \frac{2}{5} \]
They do not have the same solution.
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Based on this analysis, the correct option that consists of equations with the same solution set is the First Pair:
- \( 2(3g + 5) - 2g = 2(4 - g) \) and \( -\frac{36h}{6} = 2 \).
3 answers