Identify the pair of linear equations that have the same solution set (1 point) 2(3g + 5) - 2g = 2(4 - g) and (3k)/6 = 2; 4k - 5 = 2k and 8j - 2 = 3j; A = k/2 + 5i and (4j - 14)/2 + 5 = 3; 3(m + 1) = 10 and 6n + 3 = 6 - n

To identify the pair of linear equations that have the same solution set, we can simplify each pair of equations to see if they yield the same results for their variables.

1. **Pair 1:**
\(2(3g + 5) - 2g = 2(4 - g)\)
Simplifying:
\(6g + 10 - 2g = 8 - 2g\)
\(4g + 10 = 8 - 2g\)
Adding \(2g\) to both sides:
\(6g + 10 = 8\)
Subtracting \(10\) from both sides:
\(6g = -2\)
Dividing by \(6\):
\(g = -\frac{1}{3}\)

The second equation:
\(\frac{3k}{6} = 2\)
Simplifying gives:
\(\frac{k}{2} = 2\)
Multiplying by \(2\) results in:
\(k = 4\)

So, these two equations do not have the same solution.

2. **Pair 2:**
\(4k - 5 = 2k\)
Simplifying gives:
\(4k - 2k = 5\)
\(2k = 5\)
Dividing by \(2\):
\(k = \frac{5}{2}\)

The second equation:
\(8j - 2 = 3j\)
Simplifying gives:
\(8j - 3j = 2\)
\(5j = 2\)
Dividing by \(5\):
\(j = \frac{2}{5}\)

So, these two equations do not have the same solution.

3. **Pair 3:**
\(A = \frac{k}{2} + 5i\)

The second equation:
\(\frac{4j - 14}{2} + 5 = 3\)
Simplifying gives:
\(4j - 14 + 10 = 6\)
\(4j - 4 = 6\)
\(4j = 10\)
\(j = 2.5\)

Cannot compare since they're different variables.

4. **Pair 4:**
\(3(m + 1) = 10\)
Simplifying gives:
\(3m + 3 = 10\)
\(3m = 7\)
\(m = \frac{7}{3}\)

The second equation:
\(6n + 3 = 6 - n\)
Simplifying gives:
\(6n + n = 6 - 3\)
\(7n = 3\)
\(n = \frac{3}{7}\)

From checking each pair, we can determine that none of the pairs provided have the same solution set.

However, upon careful consideration, if we were to test pairs computationally or analytically more effectively, we say initially that **Pair 1 and Pair 4** seem to have similar structures, but we get contrasting values.

Thus, no definite pair of equations has been detected to yield identical solutions.