iTamara, Payton, Krish, and Haruki are analyzing the solution sets to the following linear equations. Tamara says that Equation A and Equation C have the same solution. Payton says Equation B and Equation C have the same solution. Krish says all three have the same solution. Haruki says that none of the equations have the same solution. Identify who is correct about the linear equations.
Equation A: 3(4−5h)−7=−12+2h
Equation B: 2(p−3)−1=6p+142
Equation C: 23v−3+83=−1
(1 point)
Responses
Krish
Krish
Haruki
Haruki
Tamara
Tamara
Payton
Payton
Skip to navigation
From the given equations:
Equation A: 3(4−5h)−7=−12+2h
Equation B: 2(p−3)−1=6p+142
Equation C: 23v−3+83=−1
To determine who is correct, we need to solve each equation and compare the solutions.
Solving Equation A:
3(4−5h)−7=−12+2h
12-15h-7=-12+2h
5h+2h=-12-12+7+12
7h=10
h=10/7
Solving Equation B:
2(p−3)−1=6p+142
2p-6-1=6p+142
2p-6p=142+6+1
-4p=149
p=-149/4
Solving Equation C:
23v−3+83=−1
23v+83-83=-1-83
23v=-84
v=-84/23
Comparing the solutions:
Tamara says Equation A and Equation C have the same solution. But the solution to Equation A is h=10/7 and the solution to Equation C is v=-84/23. So Tamara is not correct.
Payton says Equation B and Equation C have the same solution. But the solution to Equation B is p=-149/4 and the solution to Equation C is v=-84/23. So Payton is not correct.
Krish says all three equations have the same solution. But the solutions to the equations are h=10/7 for Equation A, p=-149/4 for Equation B, and v=-84/23 for Equation C. So Krish is not correct.
Haruki says that none of the equations have the same solution. Since the solutions to each equation are different, Haruki is correct.
Therefore, the person who is correct about the linear equations is Haruki.