What value is a solution to two of the equations? p/2+4=10 2=10−6h 3y−16=20 (1 point)

Question

The solution set {} is the solution to two equations.

Answer 1

To find a value that is a solution to two of the equations, we need to solve each equation for its variable.

1. For the first equation:
   \( \frac{p}{2} + 4 = 10 \)
   Subtract 4 from both sides:
   \( \frac{p}{2} = 6 \)
   Multiply both sides by 2:
   \( p = 12 \)

2. For the second equation:
   \( 2 = 10 - 6h \)
   Subtract 10 from both sides:
   \( -8 = -6h \)
   Divide by -6:
   \( h = \frac{4}{3} \)

3. For the third equation:
   \( 3y - 16 = 20 \)
   Add 16 to both sides:
   \( 3y = 36 \)
   Divide by 3:
   \( y = 12 \)

Now we can list the solutions we found:

• The solution for the first equation is \( p = 12 \).
• The solution for the second equation is \( h = \frac{4}{3} \).
• The solution for the third equation is \( y = 12 \).

The common value that is a solution to two of the equations is 12, as it is a solution to both the first and third equations.

Thus, the solution set is: \[ {12} \]