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

Question

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.