Algebra: System of non-linear equations

label Algebra
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x^2+y^2=5

x-2y=-3

May 4th, 2015

x^2+y^2=5

x-2y=-3


x=-3+2y

(-3+2y)^2+y^2=5

9-12y+4y^2+y^2=5

5y^2-12y+4=0

D=144-4*5*4=64

sqrtD=sqrt64=8

y1=(12+8)/10=2        x1=-3+2*2=1

y2=(12-8)/10=2/5      x2=-3+2*2/5=-11/5

Then substitute these roots into first equations and check if they are correct.

So, the solution is: x1=1, y1=2; x2=-11/5, y2=2/5

If you have questions feel free to contact me.


May 4th, 2015

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