To identify the number of equations that have the same solution set, we'll solve each equation for its variable and see if they yield the same solution.
Equation A:
\[ 45(3f - 7) = 25(4f - 8) \]
Expanding both sides:
\[ 135f - 315 = 100f - 200 \]
Rearranging:
\[ 135f - 100f = 315 - 200 \] \[ 35f = 115 \] \[ f = \frac{115}{35} = \frac{23}{7} \]
Equation B:
\[ 59g - 2 = 79 \]
Rearranging:
\[ 59g = 79 + 2 \] \[ 59g = 81 \] \[ g = \frac{81}{59} \]
Equation C:
\[ -2(4 - 2h) = -3(1 - h) \]
Expanding both sides:
\[ -8 + 4h = -3 + 3h \]
Rearranging:
\[ 4h - 3h = -3 + 8 \] \[ h = 5 \]
Summary of Solutions:
- Equation A has the solution \( f = \frac{23}{7} \).
- Equation B has the solution \( g = \frac{81}{59} \).
- Equation C has the solution \( h = 5 \).
All solutions are different.
Thus, the number of equations that have the same solution set is none.
Correct response: none
1 answer