##### Need algebra help for solving a system of nonlinear equations

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Solve the following system of equations

x² + y² = 7

x² - y = 5

If more than one solution need both

Nov 16th, 2015

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

when y = 1 ,  x² - y = 5

x² -1 = 5

x² = 6

when

y = -2 ,  x² - y = 5

x² --2 = 5

x²+2 =5

x² = 3

x = √6  or x = √3

y=1  or  y = -2

hope you understood..please message if you have any doubts...thank you
Nov 16th, 2015

could there be a third answer?

Nov 16th, 2015

i dont think so,only two answers will be there

x=√6 and  y=1 or

x=√3  and y= -2

Nov 16th, 2015

this is what I am being told

Nov 16th, 2015
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when y = 1 ,  x² - y = 5

x² -1 = 5

x² = 6

x = +/-√6.

x= √6 or - √6

when

y = -2 ,  x² - y = 5

x² --2 = 5

x²+2 =5

x² = 3

x = +/-√3

x=  √3 or - √3

so you can also write the solutions as

x= √6 and y = 1

x= - √6 and y = 1

x= √3 and y = -2

x=  - √3 and y = -2

Nov 16th, 2015

hi..any doubts?

Nov 16th, 2015

no everything is great

Nov 16th, 2015

if you have any doubts in this question or any new questions,please assign me as your tutor

Nov 16th, 2015

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Nov 16th, 2015
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Nov 16th, 2015
May 24th, 2017
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