What are the common solutions of

rockandriot0odjn

rockandriot0odjn

Answered question

2022-05-13

What are the common solutions of x 2 + y = 31 and y 2 + x = 41?

Answer & Explanation

odvucimo1pp17

odvucimo1pp17

Beginner2022-05-14Added 23 answers

Rearranging gives y 2 x 2 = 10 + y x , so that ( y x ) ( y + x 1 ) = 10. You don't say you are looking for integer solutions, but if you are, then you are left with finitely many possibilities for the pair ( y x , y + x 1 ) ,, which can be individually solved by Gaussian elimination: for example, one possibility is y x = 2 , y + x 1 = 5 ,, leading to y = 4 , x = 2.. But this pair does not satisy the original equations. However, another possibility is y x = 1 and y + x 1 = 10 , which leads to y = 6 and x = 5 , which does satisfy the original system. The other cases can be handled similarly.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?