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The sum of two integers is 15. Their product is 9 more than the difference of their sauares. Find the integers. If no solution explain why

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The sum of two integers is 15. Their product is 9 more than the difference of their sauares. Find the integers. If no solution explain why

anonymous · Answer

Let the integers be represented by x and y.  Try to generate equations with these variables based on the information from the sentences.

anonymous · Answer

I got 7 and 8 but it doesn't fit the 2nd reason

anonymous · Answer

Oh i think 9 and 6

anonymous · Answer

The sum of two integers is 15 is the same as saying:

x + y = 15

What equation can you think of that describes "The product of two integers is 9 more than the difference of their squares?"

anonymous · Answer

9+(x^2-y^2)

anonymous · Answer

Perfect!

Now you have a system of two equations.  What do we do next?

anonymous · Answer

Find the integers?

anonymous · Answer

That's right.  I would probably use substitution here.

anonymous · Answer

But how?

anonymous · Answer

I'll substitute the number 9,6?

anonymous · Answer

From the first equation:

x + y = 15

We can rewrite this as

y = 15 - x

For your second equation we have:

x*y = 9+(x^2-(15 - x)^2)

Substitute y = 15 - x into this equation.

x * (15 - x) = 9 + (x^2-(15 - x)^2)