SOLUTION: Find the points of intersection (x,y)of the system of nonlinear equations. x^2+y^2=5 3x-y=5

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Question 1187055: Find the points of intersection (x,y)of the system of nonlinear equations.
x^2+y^2=5
3x-y=5
Answer by MathLover1(20849) About Me  (Show Source):
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x%5E2%2By%5E2=5.........eq.1
3x-y=5..............eq.2
-------------------------------------
3x-y=5..............eq.2, solve for y
3x-5=y..............substitute in eq.1
x%5E2%2B%283x-5%29%5E2=5.........eq.1, solve for x
x%5E2%2B9x%5E2+-+30x+%2B+25=5
10x%5E2+-+30x+%2B+25-5=0
10x%5E2+-+30x+%2B+20=0.........divide by 10
x%5E2+-+3x+%2B+2=0.........factor
%28x+-+2%29+%28x+-+1%29+=+0
solutions:
if %28x+-+2%29++=+0=>x=2
if ++%28x+-+1%29+=+0=>x=1
go to
3x-y=5..............eq.2, substitute x=2
3%2A2-y=5
6-5=y
y=1
3x-y=5..............eq.2, substitute x=1
3%2A1-y=5
3-5=y
y=-2
so, solutions to the system are:
x=2, y=1
or
x=1, y=-2