SOLUTION: help me solve x+y=5 and x^2+y^2+3=0 concurrently.i

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Question 974246: help me solve x+y=5 and x^2+y^2+3=0 concurrently.i

Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
help me solve x+y=5 and x^2+y^2+3=0 concurrently.i
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y = 5-x
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Substitute for "y" and solve for "x"::
x^2 + (5-x)^2 = -3
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Comment::
The sum of two squares cannot be negative.
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No solution.
Cheers,
Stan H.
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Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=5-x from the line, substitute into the ... other equation.

x%5E2%2B%285-x%29%5E2%2B3=0

x%5E2%2B25-10x%2Bx%5E2%2B3=0

2x%5E2-10x%2B27=0

x=%2810%2B-+sqrt%28100-4%2A2%2A27%29%29%2F4

x=%2810%2B-+sqrt%28-116%29%29%2F4

x=%2810%2B-+sqrt%28-1%2A29%2A4%29%29%2F4

x=%285%2B-+sqrt%28-1%2A29%29%29%2F2
And you can evaluate the corresponding y values from these x values. The solution for any intersection is not in the x-y plane. These are complex solutions.

x=5%2F2%2B-+i%2Asqrt%2829%29%2F2