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 (1 point) Responses Krish Krish Tamara Tamara Haruki Haruki Payton

Answer 1

Let's solve each equation step-by-step to determine whose statements are correct.

Equation A: \[ 3(4 - 5h) - 7 = -12 + 2h \]

Expanding: \[ 12 - 15h - 7 = -12 + 2h \] \[ 5 - 15h = -12 + 2h \]

Rearranging gives: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \] \[ h = 1 \]

Equation B: \[ 2(p - 3) - 1 = 6p + 142 \]

Expanding: \[ 2p - 6 - 1 = 6p + 142 \] \[ 2p - 7 = 6p + 142 \]

Rearranging gives: \[ -7 - 142 = 6p - 2p \] \[ -149 = 4p \] \[ p = -\frac{149}{4} \]

Equation C: \[ 23v - 3 + 83 = -1 \]

Combining terms: \[ 23v + 80 = -1 \]

Rearranging gives: \[ 23v = -1 - 80 \] \[ 23v = -81 \] \[ v = -\frac{81}{23} \]

Summary of solutions:

• Equation A has the solution \( h = 1 \)
• Equation B has the solution \( p = -\frac{149}{4} \)
• Equation C has the solution \( v = -\frac{81}{23} \)

Now evaluating the statements:

• Tamara says Equations A and C have the same solution. Incorrect.
• Payton says Equations B and C have the same solution. Incorrect.
• Krish says all three have the same solution. Incorrect.
• Haruki says that none of the equations have the same solution. Correct.

Therefore, the correct response is: Haruki.