Question

Identify the pair of linear equations that have the same solution set. (1 point)
• 2(39 + 5) - 29 = 2(4 - g) and
= 2
• 3(m + 1) = 10 and 6n + 3 = 6 - n

04=合+5and
4J-14
+ 5 = 3

• 4k - 5 = 2k and 8j - 2 = 3j

Answer 1

To determine which pair of linear equations has the same solution set, we can rearrange each pair and analyze them.

1. **First pair:**
- \( 2(39 + 5) - 29 = 2(4 - g) \)
- Simplifying:
\[
2(44) - 29 = 2(4 - g)
\]
\[
88 - 29 = 8 - 2g
\]
\[
59 = 8 - 2g
\]
Rearranging gives:
\[
2g = 8 - 59 \Rightarrow 2g = -51 \Rightarrow g = -\frac{51}{2}
\]

2. **Second pair:**
- \( 3(m + 1) = 10 \)
- Simplifying:
\[
3m + 3 = 10 \Rightarrow 3m = 7 \Rightarrow m = \frac{7}{3}
\]

- \( 6n + 3 = 6 - n \)
- Rearranging:
\[
6n + n = 6 - 3 \Rightarrow 7n = 3 \Rightarrow n = \frac{3}{7}
\]

- The values \( m \) and \( n \) are different, so **not the same solution set.**

3. **Third pair:**
- \( 04 = k + 5 \)
- Rearranging gives:
\[
k = -1
\]

- \( 4j - 14 + 5 = 3 \)
- Simplifying gives:
\[
4j - 9 = 3 \Rightarrow 4j = 12 \Rightarrow j = 3
\]

- The values \( k \) and \( j \) are different, so **not the same solution set.**

4. **Fourth pair:**
- \( 4k - 5 = 2k \)
- Rearranging gives:
\[
4k - 2k = 5 \Rightarrow 2k = 5 \Rightarrow k = \frac{5}{2}
\]

- \( 8j - 2 = 3j \)
- Rearranging gives:
\[
8j - 3j = 2 \Rightarrow 5j = 2 \Rightarrow j = \frac{2}{5}
\]

- The values \( k \) and \( j \) are different, **not the same solution set.**

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After analyzing all the pairs, it seems none of the pairs share the same solution. Please double-check the equations provided or check if there might be some errors in typing if an option is expected to have the same solution.