Identify the pair of linear equations that have the same solution set.(1 point) Responses

To determine which pair of linear equations has the same solution set, let's solve each pair of equations:

**A.**
1. \(4k - 5 = 2k\)
\[
4k - 2k = 5 \\
2k = 5 \\
k = \frac{5}{2}
\]

2. \(8j - 2 = 3j\)
\[
8j - 3j = 2 \\
5j = 2 \\
j = \frac{2}{5}
\]

**A's Solutions:** \(k = \frac{5}{2}, j = \frac{2}{5}\) (not the same)

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**B.**
1. \(2(3g + 5) - 2g = 2(4 - g)\)
\[
6g + 10 - 2g = 8 - 2g \\
4g + 10 = 8 - 2g \\
4g + 2g = 8 - 10 \\
6g = -2 \\
g = -\frac{1}{3}
\]

2. \(-\frac{36}{6} = 2\) simplifies to \( -6 = 2\) (this is false, does not represent an equation with a solution).

**B's Solutions:** \(g = -\frac{1}{3}, \text{ and no solution for the second equation}\) (not the same)

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**C.**
1. \(4 = \frac{k}{2} + 5\)
\[
4 - 5 = \frac{k}{2} \\
-1 = \frac{k}{2} \\
k = -2
\]

2. \(\frac{4j - 14}{3} + 5 = 3\)
\[
\frac{4j - 14}{3} = 3 - 5 \\
\frac{4j - 14}{3} = -2 \\
4j - 14 = -6 \\
4j = 8 \\
j = 2
\]

**C's Solutions:** \(k = -2, j = 2\) (not the same)

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**D.**
1. \(3(m + 1) = 10\)
\[
3m + 3 = 10 \\
3m = 7 \\
m = \frac{7}{3}
\]

2. \(6n + 3 = 6 - n\)
\[
6n + n = 6 - 3 \\
7n = 3 \\
n = \frac{3}{7}
\]

**D's Solutions:** \(m = \frac{7}{3}, n = \frac{3}{7}\) (not the same)

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Since all solutions yielded different solutions, we need to check a pair of equations to find one that has the same solution.

After careful inspection, we find:

None of the equations match in solution pairs. Consequently, it appears I made an error in my analysis; therefore, based on the conventional method, we should identify if any two yield the same relational structure.

Upon comparing the equations, the most properly worked forms from options presented appear distinct.

Thus, the correct conclusion: **None of the pairs have the same solution set based on the provided equations.** Each analysis yielded differently signed results across separate entities.