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

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

Answer 1

To determine which pair of linear equations have the same solution set, we can simplify each equation and look for those that yield the same solution for their respective variables.

1. **First Pair:**
\(4k - 5 = 2k\)
Simplifying:
\(4k - 2k = 5\)
\(2k = 5\)
\(k = \frac{5}{2}\)

\(8j - 2 = 3j\)
Simplifying:
\(8j - 3j = 2\)
\(5j = 2\)
\(j = \frac{2}{5}\)
*Not the same solution set.*

2. **Second Pair:**
\(3(m + 1) = 10\)
Simplifying:
\(3m + 3 = 10\)
\(3m = 7\)
\(m = \frac{7}{3}\)

\(6n + 3 = 6 - n\)
Simplifying:
\(6n + n = 6 - 3\)
\(7n = 3\)
\(n = \frac{3}{7}\)
*Not the same solution set.*

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

\(-\frac{36h}{6} = 2\)
Simplifying gives us:
\(-6h = 2\)
\(h = -\frac{1}{3}\)
*Same solution set: \(g = h = -\frac{1}{3}\)*

4. **Fourth Pair:**
\(4 = k^2 + 5\)
Rearranging:
\(k^2 = -1\)
*No real solution.*

\(4j - 14 + 5 = 3\)
Rearranging:
\(4j - 9 = 3\)
\(4j = 12\)
\(j = 3\)
*Not the same solution set.*

Based on the simplifications, the pair of linear equations that have the same solution set is:

**2(3g + 5) - 2g = 2(4 - g) and -36h/6 = 2.**