Identify the number of equations that have the same solution set.

Question

Equation A: 45(3f−7)=25(4f−8)


Equation B: 59g−2=79


Equation C: −2(4−2h)=−3(1−h)


(1 point)
Responses

none
none

3
3

1
1

2
2

Answer 1

To find out how many equations share the same solution set, we first need to solve each equation individually for their respective variables.

Equation A: \[ 45(3f - 7) = 25(4f - 8) \]

Expanding both sides: \[ 135f - 315 = 100f - 200 \]

Now, rearranging the equation to isolate \( f \): \[ 135f - 100f = -200 + 315 \] \[ 35f = 115 \] \[ f = \frac{115}{35} = \frac{23}{7} \]

Equation B: \[ 59g - 2 = 79 \]

Adding 2 to both sides: \[ 59g = 81 \] \[ g = \frac{81}{59} \]

Equation C: \[ -2(4 - 2h) = -3(1 - h) \]

Expanding both sides: \[ -8 + 4h = -3 + 3h \]

Rearranging to isolate \( h \): \[ 4h - 3h = -3 + 8 \] \[ h = 5 \]

Now we have the solutions:

• From Equation A: \( f = \frac{23}{7} \)
• From Equation B: \( g = \frac{81}{59} \)
• From Equation C: \( h = 5 \)

Since all three equations yield different values for \( f \), \( g \), and \( h \), none of the equations have the same solution set.

Therefore, the answer is:

none