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

To identify the pair of linear equations that have the same solution set, we can solve each pair to see if they yield equivalent equations.

1. **For the first pair:**
- \(3(m+1)=10\)
\[
3m + 3 = 10 \implies 3m = 7 \implies m = \frac{7}{3}
\]
- \(6n + 3 = 6 - n\)
\[
6n + n = 6 - 3 \implies 7n = 3 \implies n = \frac{3}{7}
\]

These do not have the same solution.

2. **For the second pair:**
- \(2(3g+5)-2g=2(4-g)\)
\[
6g + 10 - 2g = 8 - 2g
\]
\[
6g - 2g + 2g = 8 - 10 \implies 6g = -2 \implies g = -\frac{1}{3}
\]
- \(-\frac{36h}{6}=2\)
\[
-6h = 2 \implies h = -\frac{1}{3}
\]

These have the same solution.

3. **For the third pair:**
- \(4 = \frac{k}{2} + 5\)
\[
4 - 5 = \frac{k}{2} \implies -1 = \frac{k}{2} \implies k = -2
\]
- \(4j - \frac{14}{3} + 5 = 3\)
\[
4j + 5 - 3 = \frac{14}{3} \implies 4j + 2 = \frac{14}{3}
\]
\[
4j = \frac{14}{3} - 2 = \frac{14}{3} - \frac{6}{3} = \frac{8}{3} \implies j = \frac{2}{3}
\]

These do not have the same solution.

4. **For the fourth pair:**
- \(4k - 5 = 2k\)
\[
4k - 2k = 5 \implies 2k = 5 \implies k = \frac{5}{2}
\]
- \(8j - 2 = 3j\)
\[
8j - 3j = 2 \implies 5j = 2 \implies j = \frac{2}{5}
\]

These do not have the same solution.

Thus, the pair of linear equations that have the same solution set is:

**2(3g+5)−2g=2(4−g) and −36h/6=2.**