Question

identify the pair of linear equations that have the same solution set.
4k-5=2k and 8j-2=3j
29(3g+5)-2g=2(4-g) and -36h over 6 =2
3(m+1)=10 and 6n +3=6-n
4=k over 2 +5 and 4j-14 over 3 +5=3

Answer 1

To identify the pairs of linear equations that have the same solution set, we need to solve each pair of equations.

1. **Equations:**
- \(4k - 5 = 2k\)
- \(8j - 2 = 3j\)

**Solving for \(k\):**
\[
4k - 2k = 5 \implies 2k = 5 \implies k = \frac{5}{2}
\]

**Solving for \(j\):**
\[
8j - 3j = 2 \implies 5j = 2 \implies j = \frac{2}{5}
\]

The solution sets are: \(k = \frac{5}{2}\) and \(j = \frac{2}{5}\), so they do not have the same solution set.

2. **Equations:**
- \(29(3g + 5) - 2g = 2(4 - g)\)
- \(-36h / 6 = 2\)

**Solving for \(g\):**
\[
29(3g + 5) - 2g = 2(4 - g)
\]
Expanding and simplifying:
\[
87g + 145 - 2g = 8 - 2g
\]
\[
89g + 145 = 8
\]
\[
89g = 8 - 145 \implies 89g = -137 \implies g = -\frac{137}{89}
\]

**Solving for \(h\):**
\[
-36h / 6 = 2 \implies -6h = 2 \implies h = -\frac{1}{3}
\]

The solution sets are: \(g = -\frac{137}{89}\) and \(h = -\frac{1}{3}\), so they do not have the same solution set.

3. **Equations:**
- \(3(m + 1) = 10\)
- \(6n + 3 = 6 - n\)

**Solving for \(m\):**
\[
3(m + 1) = 10 \implies 3m + 3 = 10 \implies 3m = 7 \implies m = \frac{7}{3}
\]

**Solving for \(n\):**
\[
6n + 3 = 6 - n \implies 6n + n = 6 - 3 \implies 7n = 3 \implies n = \frac{3}{7}
\]

The solution sets are: \(m = \frac{7}{3}\) and \(n = \frac{3}{7}\), so they do not have the same solution set.

4. **Equations:**
- \(4 = \frac{k}{2} + 5\)
- \(\frac{4j - 14}{3} + 5 = 3\)

**Solving for \(k\):**
\[
4 = \frac{k}{2} + 5 \implies \frac{k}{2} = 4 - 5 \implies \frac{k}{2} = -1 \implies k = -2
\]

**Solving for \(j\):**
\[
\frac{4j - 14}{3} + 5 = 3 \implies \frac{4j - 14}{3} = 3 - 5 \implies \frac{4j - 14}{3} = -2
\]
\[
4j - 14 = -6 \implies 4j = 8 \implies j = 2
\]

The solution sets are: \(k = -2\) and \(j = 2\), so they do not have the same solution set.

In conclusion, none of the given pairs of linear equations have the same solution set.