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 −36h6=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=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

Answer 1

To identify which pair of linear equations has the same solution set, we need to simplify each equation and check if they represent the same line.

1. **Equations**: \( 4k - 5 = 2k \) and \( 8j - 2 = 3j \)
- For the first equation:
\( 4k - 2k = 5 \)
\(\Rightarrow 2k = 5 \Rightarrow k = \frac{5}{2}\)

- For the second equation:
\( 8j - 3j = 2 \)
\(\Rightarrow 5j = 2 \Rightarrow j = \frac{2}{5}\)

- **Different solutions**.

2. **Equations**: \( 2(3g + 5) - 2g = 2(4 - g) \) and \( -\frac{36h}{6} = 2 \)
- For the first equation:
\( 6g + 10 - 2g = 8 - 2g \)
\(\Rightarrow 6g + 10 = 8 - 2g\)
\(\Rightarrow 8g = -2 \Rightarrow g = -\frac{1}{4}\)

- For the second equation:
\( -6h = 2 \Rightarrow h = -\frac{1}{3} \)

- **Different solutions**.

3. **Equations**: \( 4 = \frac{k}{2} + 5 \) and \( 4j - \frac{14}{3} + 5 = 3 \)
- For the first equation:
\( 4 - 5 = \frac{k}{2} \)
\(\Rightarrow -1 = \frac{k}{2} \Rightarrow k = -2\)

- For the second equation:
\( 4j + \frac{1}{3} = 3 \)
\(\Rightarrow 4j = \frac{8}{3} \Rightarrow j = \frac{2}{3}\)

- **Different solutions**.

4. **Equations**: \( 3(m + 1) = 10 \) and \( 6n + 3 = 6 - n \)
- For the first equation:
\( 3m + 3 = 10 \)
\(\Rightarrow 3m = 7 \Rightarrow m = \frac{7}{3}\)

- For the second equation:
\( 6n + n = 6 - 3 \Rightarrow 7n = 3 \Rightarrow n = \frac{3}{7}\)

- **Different solutions**.

Now, we can conclude. None of the pairs of equations provided have the same solution set. If any equations were incorrectly simplified or if there were typographical errors in their representation, please clarify and I can help analyze further.