SOLUTION: Help On This Will Be Great Appreciated<3 Solve The Non-Linear system of Equations. Give Exact Values. {{{x^2+y^2=10}}} {{{3y=x^2+8}}}

Algebra ->  Linear-equations -> SOLUTION: Help On This Will Be Great Appreciated<3 Solve The Non-Linear system of Equations. Give Exact Values. {{{x^2+y^2=10}}} {{{3y=x^2+8}}}       Log On


   

Question 170266: Help On This Will Be Great Appreciated<3
Solve The Non-Linear system of Equations. Give Exact Values.

x%5E2%2By%5E2=10
3y=x%5E2%2B8
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
x%5E2%2By%5E2+=+10
3y+=+x%5E2%2B8 Rewrite this as x%5E2+=+3y-8 and substitute into the 1st equation.
%283y-8%29%2By%5E2+=+10 Simplify.
y%5E2%2B3y-18+=+0 Factor.
%28y-3%29%28y%2B6%29+=+0 Apply the zero product rule.
y+=+3 or y+=+-6
Use the positive solution and substitute into the second equation to solve for x.
3y+=+x%5E2%2B8 Substitute y = 3.
3%283%29+=+x%5E2%2B8 Subtract 8 from both sides.
9-8+=+x%5E2 Take the square root of both sides.
x+=+1 or x+=+-1
The solution consists of two points of intersection:
(1, 3) and (-1, 3)
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Just for interest, since we had two solutions for y (y = 3 and y = -6), let's see what happens when we choose the second solution of y = -6 and substitute into the first equation to solve for x.
3y+=+x%5E2%2B8 Substitute y = -6.
3%28-6%29+=+x%5E2%2B8 Subtract 8 from both sides.
x%5E2+=+-26 Take the square root of both sides.
x+=+sqrt%28-26%29 or x+=+-sqrt%28-26%29 and, as you can see, the results are "imaginary" numbers, so there is no "real" solution for y = -6.
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Let's see what the graph of these two functions look like: