SOLUTION: What is the solution of the​ system? Find the ordered pair x^2+y^2=4 x+y=1

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Question 1134167: What is the solution of the​ system? Find the ordered pair
x^2+y^2=4
x+y=1
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
y=1-x
substitute
x^2+(1-x)^2=4
x^2+1-2x+x^2=4
2x^2-2x-3=0
x=(1/4)(2+/- sqrt (4+24))
=(1/4)(2+/-2 sqrt (7)
or 0.5+/-0.5 sqrt (7)
numerically 1.82 and -0.82 for x
y=-0.82 and 3.15
(1.82, -0.82) and (-0.82, 1.82)
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C1-x%2Csqrt%284-x%5E2%29%2C-sqrt%284-x%5E2%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2=4....eq.1
x%2By=1.......eq.2
-------------------------
x%2By=1.......eq.2...solve for y
y=1-x.......substitute in eq.1

x%5E2%2B%281-x%29%5E2=4....eq.1...solve for x
x%5E2%2B1-2x%2Bx%5E2=4
2x%5E2-2x+%2B1-4=0
2x%5E2-2x+-3=0....use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A2%2A%28-3%29+%29%29%2F%282%2A2%29+
x+=+%282+%2B-+sqrt%28+4%2B24+%29%29%2F4+
x+=+%282+%2B-+sqrt%28+7%2A4+%29%29%2F4+
x+=+%282+%2B-+2sqrt%28+7+%29%29%2F4+
x+=+%281+%2B-+sqrt%28+7+%29%29%2F2+
solutions:
x+=+%281+%2B+sqrt%28+7+%29%29%2F2+
x+=+%281+-+sqrt%28+7+%29%29%2F2+

go to
y=1-x.......eq.2...plug in x+=+%281+%2B+sqrt%28+7+%29%29%2F2+

y=1-%281+%2B+sqrt%28+7+%29%29%2F2

y=2%2F2-1%2F2+%2B+sqrt%28+7+%29%2F2
y=1%2F2+%2B+sqrt%28+7+%29%2F2
y=%281+%2B+sqrt%28+7+%29%29%2F2


y=1-x.......eq.2...plug in x+=+%281+-+sqrt%28+7+%29%29%2F2+

y=1-%281+-+sqrt%28+7+%29%29%2F2

y=2%2F2-1%2F2+-+sqrt%28+7+%29%2F2
y=1%2F2+-+sqrt%28+7+%29%2F2
y=%281+-+sqrt%28+7+%29%29%2F2

ordered pairs are:
(+1%2F2+-+sqrt%287%29%2F2, +1%2F2+%2B+sqrt%287%29%2F2) ≈(+-0.8, +1.8)
(+1%2F2+%2Bsqrt%287%29%2F2, +1%2F2+-+sqrt%287%29%2F2) ≈ (++1.8, +-0.8)