Identify the pair of linear equations that have the same solution set (1 point)
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
The pair of linear equations that have the same solution set is:
4k - 5 = 2k and 8j - 2 = 3j
To identify the pair of linear equations that have the same solution set, we can solve each pair of equations separately and compare the solution sets.
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.
The pair of linear equations that have the same solution set is:
3(m + 1) = 10 and 6n + 3 = 6 - n