Question

What value is a solution to two of the equations?

p2+4=10

2=10−6h

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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}.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the solution to the two equations, we can solve each equation separately.

1. p^2 + 4 = 10
Subtracting 4 from both sides:
p^2 = 6
Taking the square root of both sides:
p = ±√6

Therefore, the value of p that is a solution to this equation is p = ±√6.

2. 2 = 10 - 6h
Adding 6h to both sides:
2 + 6h = 10
Subtracting 2 from both sides:
6h = 8
Dividing both sides by 6:
h = 8/6
Simplifying:
h = 4/3

Therefore, the value of h that is a solution to this equation is h = 4/3.

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

Therefore, the value of y that is a solution to this equation is y = 12.

So, the solution set { } is the solution to two equations is:
p = ±√6 and h = 4/3.

Answer 3

[AI-generated answer — Explain Bot]

To find the value that is a solution to two equations, we will solve each equation separately and check for any common values.

1) p^2 + 4 = 10:
To solve this equation, we'll start by subtracting 4 from both sides:
p^2 = 6
Next, we'll take the square root of both sides, considering both positive and negative solutions:
p = ±√6

2) 2 = 10 - 6h:
We can simplify this equation by adding 6h to both sides:
6h + 2 = 10
Then, subtract 2 from both sides:
6h = 8
Finally, divide both sides by 6 to solve for h:
h = 8/6 = 4/3

3) 3y - 16 = 20:
First, we'll add 16 to both sides of the equation:
3y = 36
Next, divide both sides by 3 to find the value of y:
y = 12

Now, let's check for any common values among the solutions we found:
p = ±√6
h = 4/3
y = 12

From the given equations, it appears that there are no common values among these three solutions. Therefore, the solution set { } is empty.