HelpfulTutor

We can simplifify this equation first. 

x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14

x+8y=13+2y+2y^2 -7y-14

x+8y=2y+2y^2 -7y -1

x+6y=2y^2 - 7y - 1

x+13y=2y^2-2

x=2y^2-13y-1

Then we can write this into vertex form, try this part yourself! 

If needed, help for this step can be found through MathWay.

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Here it is! (13/4, -177/8)

Wondeful thinking BlackjackEd!

However, there is an alternative method:

3X=81 x 5

We could first divide both sides by 3 and get

X=27 x 5

This also gives us 135.

Okay. Let's consider the siblings as A1 and A2, B1 and B2, C1 and C2. SInce they are sitting in two rows we will fill the first row in first. So A1 is in the first, B1 is in the second, and C1 is in the third. Now we move on to the second row which is A2, B2, and C2. 

However, there is another possible arrangement for the first row. That is A2 for the first, B1 for the second, and C1 for the third. Then the second row is A1, B2, and C2. 

These are the only two possible arrangments that will satisy the conditions given. Thus, there are two ways to seat three siblings so that siblings don't sit next to each other.