What value is a solution to two of the equations?

Question

p/2+4=10


2=10−6h


3y−16=20


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

Answer 1

To find a common value that satisfies two of the given equations, we will solve each equation step by step.

1. For the equation \( \frac{p}{2} + 4 = 10 \): \[ \frac{p}{2} = 10 - 4 \] \[ \frac{p}{2} = 6 \] \[ p = 6 \times 2 = 12 \] So, \( p = 12 \).

2. For the equation \( 2 = 10 - 6h \): \[ 6h = 10 - 2 \] \[ 6h = 8 \] \[ h = \frac{8}{6} = \frac{4}{3} \] So, \( h = \frac{4}{3} \).

3. For the equation \( 3y - 16 = 20 \): \[ 3y = 20 + 16 \] \[ 3y = 36 \] \[ y = \frac{36}{3} = 12 \] So, \( y = 12 \).

Now we have the solutions:

• \( p = 12 \)
• \( h = \frac{4}{3} \)
• \( y = 12 \)

The values of \( p \) and \( y \) both equal \( 12 \). Thus, the solution set that satisfies two of the equations is:

\[ {12} \]