Need algebra help for solving a system of nonlinear equations

User Generated

cgureevna

Mathematics

Description

Solve the following system of equations

x² + y² = 7

x² - y = 5

If more than one solution need both

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Explanation & Answer

hello

x² + y² = 7

x² - y = 5


take second equation, x² - y = 5

                                    x² = 5+y


substitite x² = 5+y in  x² + y² = 7

                                   5+y + y² = 7

                                  y²+y - 2=0

                                  y² -y+2y-2 = 0

                                 y(y-1) +2 (y-1) =0

                                 (y-1) = 0   or y+2 = 0

                                   y=1  or  y = -2..................................ANSWER


when y = 1 ,  x² - y = 5

                     x² -1 = 5

                    x² = 6

                     x = √6.....................................ANSWER

when 

y = -2 ,  x² - y = 5

              x² --2 = 5

               x²+2 =5

             x² = 3

               x = √3.....................................ANSWER


ANSWER IS

x = √6  or x = √3

 y=1  or  y = -2

  



hope you understood..please message if you have any doubts...thank you


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