Question

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

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

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

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

Answer 1

To determine which pair of linear equations has the same solution set, we need to manipulate and analyze each pair.

1. **3(m + 1) = 10**
This simplifies to:
\(3m + 3 = 10\)
\(3m = 10 - 3\)
\(3m = 7\)
\(m = \frac{7}{3}\)

**6n + 3 = 6 - n**
This simplifies to:
\(6n + n = 6 - 3\)
\(7n = 3\)
\(n = \frac{3}{7}\)

**Conclusion**: Different solutions.

2. **2(3g + 5) - 2g = 2(4 - g)**
Simplifying:
\(6g + 10 - 2g = 8 - 2g\)
\(4g + 10 = 8 - 2g\)
\(4g + 2g = 8 - 10\)
\(6g = -2\)
\(g = -\frac{1}{3}\)

**−36h6 = 2**
This simplifies to:
\(-6h = 2\)
\(h = -\frac{1}{3}\)

**Conclusion**: Same solution.

3. **4 = \frac{k}{2} + 5**
This simplifies to:
\(\frac{k}{2} = 4 - 5\)
\(\frac{k}{2} = -1\)
\(k = -2\)

**\frac{4j - 14}{3} + 5 = 3**
This simplifies to:
\(\frac{4j - 14}{3} = 3 - 5\)
\(\frac{4j - 14}{3} = -2\)
\(4j - 14 = -6\)
\(4j = 8\)
\(j = 2\)

**Conclusion**: Different solutions.

4. **4k - 5 = 2k**
This simplifies to:
\(4k - 2k = 5\)
\(2k = 5\)
\(k = \frac{5}{2}\)

**8j - 2 = 3j**
This simplifies to:
\(8j - 3j = 2\)
\(5j = 2\)
\(j = \frac{2}{5}\)

**Conclusion**: Different solutions.

Based on this analysis, the only pair of equations that have the same solution set is:

**2(3g + 5) - 2g = 2(4 - g)** and **−36h6 = 2.**