To determine which pair of linear equations has the same solution set, we can solve each pair of equations and see if they lead to the same result.
1. For \(4k - 5 = 2k\):
\[
4k - 2k = 5 \implies 2k = 5 \implies k = \frac{5}{2}
\]
For \(8j - 2 = 3j\):
\[
8j - 3j = 2 \implies 5j = 2 \implies j = \frac{2}{5}
\]
So the solutions are \(k = \frac{5}{2}\) and \(j = \frac{2}{5}\), which are different.
2. For \(2(3g + 5) - 2g = 2(4 - g)\):
\[
6g + 10 - 2g = 8 - 2g \implies 4g + 10 = 8 \implies 4g = -2 \implies g = -\frac{1}{2}
\]
And for \(-\frac{36h}{6} = 2\):
\[
-6h = 2 \implies h = -\frac{1}{3}
\]
So the solutions are \(g = -\frac{1}{2}\) and \(h = -\frac{1}{3}\), which are different.
3. For \(4 = \frac{k}{2} + 5\):
\[
\frac{k}{2} = 4 - 5 \implies \frac{k}{2} = -1 \implies k = -2
\]
And for \(\frac{4j - 14}{3} + 5 = 3\):
\[
\frac{4j - 14}{3} = 3 - 5 \implies \frac{4j - 14}{3} = -2 \implies 4j - 14 = -6 \implies 4j = 8 \implies j = 2
\]
So the solutions are \(k = -2\) and \(j = 2\), which are different.
4. For \(3(m + 1) = 10\):
\[
3m + 3 = 10 \implies 3m = 7 \implies m = \frac{7}{3}
\]
For \(6n + 3 = 6 - n\):
\[
6n + n = 6 - 3 \implies 7n = 3 \implies n = \frac{3}{7}
\]
So the solutions are \(m = \frac{7}{3}\) and \(n = \frac{3}{7}\), which are different.
Based on this analysis, none of the pairs of equations have the same solution set. However, if you are looking for pairs where the transformation leads to a similar structure while still yielding distinct solutions, it could also be relevant.
Therefore, none of the pairs match. If there is a missing calculation or rephrasing in your question, could you clarify or check the equations again?