SOLUTION: (x-4)^(2)+(y-5)^(2)=8 (x+1)^(2)+(Y+2)^(2)=34 Please help me to solve this system of equations

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: (x-4)^(2)+(y-5)^(2)=8 (x+1)^(2)+(Y+2)^(2)=34 Please help me to solve this system of equations      Log On


   

Question 678465: (x-4)^(2)+(y-5)^(2)=8
(x+1)^(2)+(Y+2)^(2)=34
Please help me to solve this system of equations
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-4%29%5E2%2B%28y-5%29%5E2=8...........1
%28x%2B1%29%5E2%2B%28y%2B2%29%5E2=34..........2
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x%5E2-8x%2B16%2By%5E2-10y%2B25=8...........1
x%5E2%2By%5E2-8x-10y%2B41=8
x%5E2%2By%5E2-8x-10y=-33..............1a


%28x%5E2%2B2x%2B1%29%2B%28y%5E2%2B4y%2B4%29=34..........2
x%5E2%2By%5E2%2B2x%2B4y%2B5=34
x%5E2%2By%5E2%2B2x%2B4y=29............2a
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take 1a and 2a and subtract
x%5E2%2By%5E2-8x-10y=-33..............1a

x%5E2%2By%5E2%2B2x%2B4y=29............2a
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x%5E2-x%5E2%2By%5E2-y%5E2-8x-2x-10y-4y=-33-29

-10x-14y=-62......both sides multiply by -1

10x%2B14y=62........solve for x

10x=-14y%2B62

x=-14y%2F10%2B62%2F10

x=-1.4y%2B6.2.......plug in 1a

%28-1.4y%2B6.2%29%5E2%2By%5E2-8%28-1.4y%2B6.2%29-10y=-33.......1a..solve for y

1.96y%5E2-17.36y%2B38.44%2By%5E2%2B11.2y-49.6-10y=-33

2.96y%5E2-16.16y-11.16=-33

2.96y%5E2-16.16y%2B21.84=0....use quadratic formula

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



y+=+%2816.16+%2B-+sqrt%28261.1456-258.586+%29%29%2F5.92+

y+=+%2816.16+%2B-+sqrt%282.5596+%29%29%2F5.92+

y+=+%2816.16+%2B-+1.59987%29%2F5.92+

solutions:

y+=+%2816.16+%2B+1.59987%29%2F5.92+

y+=17.75987%2F5.92+

highlight%28y+=2.99998%29+

and

y+=+%2816.16+-+1.59987%29%2F5.92+

y+=14.56013%2F5.92+

highlight%28y+=2.45948%29+

now find x

x=-1.4y%2B6.2......plug in y+=2.99998+

x=-1.4%2A2.99998%2B6.2

highlight%28x=2.000028%29

and

x=-1.4y%2B6.2......plug in y+=2.45948+

x=-1.4%2A2.45948%2B6.2

highlight%28x=2.756728%29