The pair of linear equations that have the same solution set is:
4k - 5 = 2k and 8j - 2 = 3j
2(3g + 5) - 2g = 2(4 - g) and (- 36h)/6 = 2
4 = k/2 + 5 and (4j - 14)/3 + 5 = 3
4k - 5 = 2k and 8j - 2 = 3j
3(m + 1) = 10 and 6n + 3 = 6 - n
4k - 5 = 2k and 8j - 2 = 3j
Let's solve the first pair of equations:
2(3g + 5) - 2g = 2(4 - g)
6g + 10 - 2g = 8 - 2g
4g + 10 = 8
4g = -2
g = -2/4
g = -1/2
(- 36h)/6 = 2
-6h = 12
h = 12/-6
h = -2
From the first pair of equations, we found that g = -1/2 and h = -2.
Now, let's solve the second pair of equations:
4 = k/2 + 5
4 - 5 = k/2
-1 = k/2
k/2 = -1
k = -2
(4j - 14)/3 + 5 = 3
4j - 14 + 15 = 9
4j + 1 = 9
4j = 9 - 1
j = 8/4
j = 2
From the second pair of equations, we found that k = -2 and j = 2.
Finally, let's solve the third pair of equations:
4k - 5 = 2k
4k - 2k = 5
2k = 5
k = 5/2
8j - 2 = 3j
8j - 3j = 2
5j = 2
j = 2/5
From the third pair of equations, we found that k = 5/2 and j = 2/5.
The solution sets are:
For the first pair: g = -1/2, h = -2
For the second pair: k = -2, j = 2
For the third pair: k = 5/2, j = 2/5
Comparing the solution sets, we can see that the pair of equations (4 = k/2 + 5) and ((4j - 14)/3 + 5 = 3) have the same solution set.
3(m + 1) = 10 and 6n + 3 = 6 - n