What value is a solution to two of the equations?

Question

p2+4=10

2=10−6h

3y−16=20
The solution set { } is the solution to two equations.

Answer 1

To find the solution set, we need to solve each equation separately and see if there are any common values for the variables.

1) p^2 + 4 = 10
Subtracting 4 from both sides:
p^2 = 6
Taking the square root of both sides (considering both positive and negative square roots since no clarification is given):
p = ±√6

2) 2 = 10 - 6h
Subtracting 10 from both sides:
-8 = -6h
Dividing by -6 (and changing the sign):
8/6 = h
4/3 = h

3) 3y - 16 = 20
Adding 16 to both sides:
3y = 36
Dividing by 3:
y = 12

Now, let's see if there are any common values among these solutions:

{±√6, 4/3, 12}

After comparing the solutions, we see that the value 12 is the solution common to equations 2 and 3. Thus, the solution set is {12}.