Question

Identify the pair of linear equations that have the same solution set.(1 point)
Choose One Of The Following Responses That's Close To The Answer

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

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

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 that have the same solution set, we need to solve each option and see if the equations in each pair are equivalent.
Let's analyze the pairs one by one:

1. **3(m+1)=10 and 6n+3=6−n**
- For the first equation:
\[
3(m + 1) = 10 \implies 3m + 3 = 10 \implies 3m = 7 \implies m = \frac{7}{3}
\]
- For the second equation:
\[
6n + 3 = 6 - n \implies 6n + n = 6 - 3 \implies 7n = 3 \implies n = \frac{3}{7}
\]
- Not the same solution set.

2. **4 = k/2 + 5 and (4j−14)/3 + 5 = 3**
- For the first equation:
\[
4 = \frac{k}{2} + 5 \implies \frac{k}{2} = -1 \implies k = -2
\]
- For the second equation:
\[
\frac{4j - 14}{3} + 5 = 3 \implies \frac{4j - 14}{3} = -2 \implies 4j - 14 = -6 \implies 4j = 8 \implies j = 2
\]
- Not the same solution set.

3. **4k−5=2k and 8j−2=3j**
- For the first equation:
\[
4k - 5 = 2k \implies 4k - 2k = 5 \implies 2k = 5 \implies k = \frac{5}{2}
\]
- For the second equation:
\[
8j - 2 = 3j \implies 8j - 3j = 2 \implies 5j = 2 \implies j = \frac{2}{5}
\]
- Not the same solution set.

4. **2(3g+5)−2g=2(4−g) and −36h/6=2**
- For the first equation:
\[
2(3g + 5) - 2g = 2(4 - g) \implies 6g + 10 - 2g = 8 - 2g \implies 4g + 10 = 8 \implies 4g = -2 \implies g = -\frac{1}{2}
\]
- For the second equation:
\[
-\frac{36h}{6} = 2 \implies -6h = 2 \implies h = -\frac{1}{3}
\]
- Not the same solution set.

Based on the above calculations, **none of the pairs of equations provided** have the same solution set. If you would like me to check specific values or clarify further, please provide additional context.