Identify the pair of linear equations that have the same solution set.

Question

A. 3(m+1)=10 and 6n+3=6−n
3 left parenthesis m plus 1 right parenthesis equals 10 and 6 n plus 3 equals 6 minus n

B. 2(3g+5)−2g=2(4−g) and −36h6=2
2 left parenthesis 3 g plus 5 right parenthesis minus 2 g equals 2 left parenthesis 4 minus g right parenthesis and Start Fraction negative 36 h over 6 End Fraction equals 2

C. 4=k2+5 and 4j−143+5=3
4 equals Start Fraction k over 2 End Fraction plus 5 and Start Fraction 4 j minus 14 over 3 End Fraction plus 5 equals 3

D. 4k−5=2k and 8j−2=3j

Answer 1

The correct answer is C.

Answer 2

Tamara, 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

Answer 3

To determine who is correct, we need to compare the solution sets of the three equations.

Equation A: 3(4−5h)−7=−12+2h
Equation B: 2(p−3)−1=6p+142
Equation C: 23v−3+83=−1

To find the solution sets of the equations, we need to solve each equation for its variable.

Equation A:
3(4−5h)−7=−12+2h
12 - 15h - 7 = -12 + 2h
5h -9 = -12 + 2h
3h = -15
h = -5

Equation B:
2(p−3)−1=6p+142
2p - 6 - 1 = 6p + 142
2p - 7 = 6p + 142
-4p = 149
p = -37.25

Equation C:
23v−3+83=−1
23v + 80 = -1
23v = -81
v = -3.52

Now, let's compare the solution sets:

Solution to Equation A: h = -5
Solution to Equation B: p = -37.25
Solution to Equation C: v = -3.52

It is clear that none of the solutions are the same. Therefore, Haruki is correct in saying that none of the equations have the same solution.