Identify the pair of linear equations that have the same solution set.
Responses
4=k/2+5 and 4j−14/3+5=3
4 is equal to k over 2 plus 5 and the fraction with numerator 4 j minus 14 and denominator 3 plus 5 is equal to 3
4k−5=2k and 8j−2=3j
4 k minus 5 is equal to 2 k and 8 j minus 2 is equal to 3 j
3(m+1)=10 and 6n+3=6−n
3 times open paren m plus 1 close paren is equal to 10 and 6 n plus 3 is equal to 6 minus n
2(3g+5)−2g=2(4−g) and −36h/6=2
2(3g+5)−2g=2(4−g) and −36h/6=2
The pair of linear equations that have the same solution set is:
2(3g+5)−2g=2(4−g) and −36h/6=2
To identify the pair of linear equations that have the same solution set, we need to simplify each equation and find if they are equivalent to each other. Let's break down each option and determine which one satisfies the condition.
1) 4 = k/2 + 5 and 4j - 14/3 + 5 = 3
Simplifying the first equation:
4 = k/2 + 5
Subtracting 5 from both sides: -1 = k/2
Multiplying both sides by 2: -2 = k
Simplifying the second equation:
4j - 14/3 + 5 = 3
Adding 14/3 and 5 to both sides: 4j + 14/3 = 8/3
Finding a common denominator and simplifying: 12j + 14 = 8
Subtracting 14 from both sides: 12j = -6
Dividing both sides by 12: j = -1/2
Since k = -2 and j = -1/2, the solution set for this pair of equations is different. So, option 1 is not the correct answer.
2) 4k - 5 = 2k and 8j - 2 = 3j
Simplifying the first equation:
4k - 5 = 2k
Subtracting 2k from both sides: 2k - 5 = 0
Adding 5 to both sides: 2k = 5
Dividing both sides by 2: k = 5/2
Simplifying the second equation:
8j - 2 = 3j
Subtracting 3j from both sides: 5j - 2 = 0
Adding 2 to both sides: 5j = 2
Dividing both sides by 5: j = 2/5
Since k = 5/2 and j = 2/5, the solution set for this pair of equations is different too. Therefore, option 2 is also not the correct answer.
3) 3(m + 1) = 10 and 6n + 3 = 6 - n
Simplifying the first equation:
3(m + 1) = 10
Distributing: 3m + 3 = 10
Subtracting 3 from both sides: 3m = 7
Dividing both sides by 3: m = 7/3
Simplifying the second equation:
6n + 3 = 6 - n
Adding n to both sides: 7n + 3 = 6
Subtracting 3 from both sides: 7n = 3
Dividing both sides by 7: n = 3/7
Since m = 7/3 and n = 3/7, the solution set for this pair of equations is the same. Thus, option 3 is the correct answer.
4) 2(3g + 5) - 2g = 2(4 - g) and -36h/6 = 2
Simplifying the first equation:
2(3g + 5) - 2g = 2(4 - g)
Distributing: 6g + 10 - 2g = 8 - 2g
Combining like terms: 4g + 10 = 8
Subtracting 10 from both sides: 4g = -2
Dividing both sides by 4: g = -1/2
Simplifying the second equation:
-36h/6 = 2
Multiplying both sides by 6: -36h = 12
Dividing both sides by -36: h = -1/3
Since g = -1/2 and h = -1/3, the solution set for this pair of equations is different. Therefore, option 4 is not the correct answer.
Therefore, the pair of linear equations that have the same solution set is option 3: 3(m + 1) = 10 and 6n + 3 = 6 - n.