Question

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

4=k2+5 and 4j−143+5=3
4 equals Start Fraction k over 2 End Fraction plus 5 and Start Fraction 4 j minus 14 over 3 End Fraction plus 5 equals 3

3(m+1)=10 and 6n+3=6−n
3 left parenthesis m plus 1 right parenthesis equals 10 and 6 n plus 3 equals 6 minus n

4k−5=2k and 8j−2=3j
4 k minus 5 equals 2 k and 8 j minus 2 equals 3 j

2(3g+5)−2g=2(4−g) and −36h6=2

Answer 1

To identify the pair of linear equations with the same solution set, we need to analyze each pair:

1. **First Pair:**
\( 4 = \frac{k}{2} + 5 \) and \( \frac{4j - 14}{3} + 5 = 3 \)
**First Equation:**
Rearranging:
\( \frac{k}{2} = 4 - 5 = -1 \)
\( k = -2 \)
**Second Equation:**
Rearranging:
\( \frac{4j - 14}{3} = 3 - 5 = -2 \)
\( 4j - 14 = -6 \)
\( 4j = 8 \)
\( j = 2 \)

The first pair does not have the same solution set.

2. **Second Pair:**
\( 3(m + 1) = 10 \) and \( 6n + 3 = 6 - n \)
**First Equation:**
\( 3m + 3 = 10 \)
\( 3m = 7 \)
\( m = \frac{7}{3} \)
**Second Equation:**
Rearranging:
\( 6n + n = 6 - 3 \)
\( 7n = 3 \)
\( n = \frac{3}{7} \)

The second pair does not have the same solution set.

3. **Third Pair:**
\( 4k - 5 = 2k \) and \( 8j - 2 = 3j \)
**First Equation:**
Rearranging:
\( 4k - 2k = 5 \)
\( 2k = 5 \)
\( k = \frac{5}{2} \)
**Second Equation:**
Rearranging:
\( 8j - 3j = 2 \)
\( 5j = 2 \)
\( j = \frac{2}{5} \)

The third pair does not have the same solution set.

4. **Fourth Pair:**
\( 2(3g + 5) - 2g = 2(4 - g) \) and \( -36h = 6 \)
**First Equation:**
\( 6g + 10 - 2g = 8 - 2g \) or simplified:
\( 6g + 2g - 2g = 8 - 10 \)
\( 6g = -2 \)
\( g = -\frac{1}{3} \)
**Second Equation:**
\( -36h = 6 \)
\( h = -\frac{1}{6} \)

The fourth pair does not have the same solution set.

**Conclusion:**
None of the given pairs of equations have the same solution set based on the calculations above.

Please let me know if you need further analysis or clarification!