Identify the pair of linear equations that have the same solution set:

Question

1. 4k-5=2k and 8j-2=3j
2. 3(m+1) =10 and 6n+3=6-n
3. 2(3g+5)-2g=2 (4g-2g) and -36h/6=2
4. 4=k/2+5 and 4j/3-14/3 +5=3

Answer 1

To determine which pair of linear equations has the same solution set, we will solve each pair of equations.

1.
Equation 1: \(4k - 5 = 2k\)
Rearranging gives:
\(4k - 2k = 5\)
\(2k = 5\)
\(k = \frac{5}{2}\)

Equation 2: \(8j - 2 = 3j\)
Rearranging gives:
\(8j - 3j = 2\)
\(5j = 2\)
\(j = \frac{2}{5}\)

Solution Set: Different solutions (\(k = \frac{5}{2}\), \(j = \frac{2}{5}\))

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2.
Equation 1: \(3(m + 1) = 10\)
Distributing gives:
\(3m + 3 = 10\)
\(3m = 7\)
\(m = \frac{7}{3}\)

Equation 2: \(6n + 3 = 6 - n\)
Rearranging gives:
\(6n + n = 6 - 3\)
\(7n = 3\)
\(n = \frac{3}{7}\)

Solution Set: Different solutions (\(m = \frac{7}{3}\), \(n = \frac{3}{7}\))

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3.
Equation 1: \(2(3g + 5) - 2g = 2(4g - 2g)\)
Distributing gives:
\(6g + 10 - 2g = 4g - 4g\)
Combining terms:
\(4g + 10 = 0\)
\(4g = -10\)
\(g = -\frac{5}{2}\)

Equation 2: \(-\frac{36h}{6} = 2\)
Simplifying gives:
\(-6h = 2\)
\(h = -\frac{1}{3}\)

Solution Set: Different solutions (\(g = -\frac{5}{2}\), \(h = -\frac{1}{3}\))

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4.
Equation 1: \(4 = \frac{k}{2} + 5\)
Rearranging gives:
\(\frac{k}{2} = 4 - 5\)
\(\frac{k}{2} = -1\)
\(k = -2\)

Equation 2: \(\frac{4j}{3} - \frac{14}{3} + 5 = 3\)
Rearranging gives:
\(\frac{4j}{3} - \frac{14}{3} + \frac{15}{3} = 3\)
\(\frac{4j + 1}{3} = 3\)
\(4j + 1 = 9\)
\(4j = 8\)
\(j = 2\)

Solution Set: Different solutions (\(k = -2\), \(j = 2\))

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Conclusion:

All four pairs yield different solutions. None of the pairs of linear equations presented have the same solution set.