To determine who among Tamara, Payton, Krish, and Haruki is correct about the linear equations, let's solve each of the equations one by one.
Equation A:
\[ 3(4 - 5h) - 7 = -12 + 2h \]
- Distribute: \[ 12 - 15h - 7 = -12 + 2h \]
- Simplify: \[ 5 - 15h = -12 + 2h \]
- Rearranging gives: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \]
- Solving for h: \[ h = 1 \]
Equation B:
\[ 2(p - 3) - 1 = \frac{6p + 14}{2} \]
- Distribute: \[ 2p - 6 - 1 = 3p + 7 \]
- Simplifying gives: \[ 2p - 7 = 3p + 7 \]
- Rearranging gives: \[ -7 - 7 = 3p - 2p \] \[ -14 = p \]
- So, \( p = -14 \).
Equation C:
\[ \frac{2}{3}v - 3 + \frac{8}{3} = -1 \]
- Combine constants: \[ \frac{2}{3}v + \frac{8}{3} - 3 = -1 \] \[ \frac{2}{3}v + \frac{8 - 9}{3} = -1 \] \[ \frac{2}{3}v - \frac{1}{3} = -1 \]
- Adding \( \frac{1}{3} \): \[ \frac{2}{3}v = -1 + \frac{1}{3} \] \[ \frac{2}{3}v = -\frac{3}{3} + \frac{1}{3} \] \[ \frac{2}{3}v = -\frac{2}{3} \]
- Multiplying by \( \frac{3}{2} \): \[ v = -1 \]
Summary of Solutions:
- Equation A: \( h = 1 \)
- Equation B: \( p = -14 \)
- Equation C: \( v = -1 \)
Analyzing the Claims:
- Tamara (Equation A and Equation C have the same solution): Incorrect
- A: \( h = 1 \), C: \( v = -1 \) (different solutions)
- Payton (Equation B and Equation C have the same solution): Incorrect
- B: \( p = -14 \), C: \( v = -1 \) (different solutions)
- Krish (All three have the same solution): Incorrect
- All solutions are different.
- Haruki (None of the equations have the same solution): Correct
- All three equations have different solutions.
Final Answer: Haruki is correct.
1 answer