Question 299957: This is a non-linear system
It says solve this sytem two ways: 1. Algebraically
2. Graphically
Problem: x^2+Y^2=4
x+y=4
I used the substitution method and got this
original problem:
x^2+y^2=4
x+y=4
x+y=4
-x =-x
y=4-x
x^2+(4-x)^2=4
x^2+16-8x+x^2-4=0
2x^2-8x+12=0
2(x^2-4x+6)=0
My math teacher gaves us a hint. He said that first break it down and that it won't factor. Then to use the the quadratic formula to graph it. So since it wont factor out I solved it using the quadratic formula and got 2 +/- i Square root 8.
Don't know if I did it right and if so how do I graph it?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve this sytem two ways:
1. Algebraically
2. Graphically
Problem:
x^2+Y^2=4
x+y=4
-------------------
x = 4-y
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Substitute in the 1st equation:
(4-y)^2 + y^2 = 4
16-8y+y^2+y^2 = 4
---
2y^2 - 8y + 12 = 0
Divide by 2 and solve for "y":
y^2 - 4y + 6 = 0
y = [4+-sqrt(16-4*6)]/2
y = [4+-sqrt(-8)]/2
y = 2+isqrt(2) or y = 2-isqrt(2)
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Substitute in x = 4-y:
When y = 2+isqrt(2), x = 2-isqrt(2)
When y = 2-isqrt(2), x = 2+isqrt(2)
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Cheers,
Stan H.
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