Question

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

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 −36h/6=2
2 left parenthesis 3 g plus 5 right parenthesis minus 2 g equals 2 left parenthesis 4 minus g right parenthesis and Start Fraction negative 36 h over 6 End Fraction equals 2

4=k/2+5
and 4j−14/3+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

Answer 1

To determine which pair of linear equations has the same solution set, we can simplify and solve each pair of equations.

1. **First pair:**
- \( 4k - 5 = 2k \)
\[
4k - 2k = 5 \implies 2k = 5 \implies k = \frac{5}{2}
\]
- \( 8j - 2 = 3j \)
\[
8j - 3j = 2 \implies 5j = 2 \implies j = \frac{2}{5}
\]
- **Different solutions.**

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

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

4. **Fourth pair:**
- \( 3(m + 1) = 10 \)
\[
3m + 3 = 10 \implies 3m = 7 \implies m = \frac{7}{3}
\]
- \( 6n + 3 = 6 - n \)
\[
6n + n = 6 - 3 \implies 7n = 3 \implies n = \frac{3}{7}
\]
- **Different solutions.**

After analyzing each pair, none of the provided pairs have the same solution set.

Since none produce the same solution, please double-check the options or provide further context for exploration.