Question 40824: how do you solve this system of equation:
x^2+y^2=36
x+y=4
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Well, graphing might help but is often not precise enough to give a perfect solution...your best bet is to do it using algebra by solving the second equation for x or y and then plugging it in to the first...like this...
x^2+y^2=36
x+y=4
gives
y = 4 - x and
x^2 + (4 - x)^2 = 36
x^2 + 16 - 8x + x^2 = 36
2x^2 - 8x - 20 = 0
x^2 - 4x - 10 = 0 (can't factor, use quadratic)
x = (4 ± sqrt(16 + 40)) / 2
x = (4 ± 2*sqrt(14)) / 2
x = 2 ± sqrt(14)
Now plug either of these solutions into the second eqn to get the y's that correspond to each x...
y = 4 - (2 + sqrt(14) = 2 - sqrt(14)
y = 4 - (2 - sqrt(14) = 2 + sqrt(14)
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