SOLUTION: find the point of intersections of (x-1)^2+(y-3)^2=10,x^2+(y+1)^2=5

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Question 1044078: find the point of intersections of (x-1)^2+(y-3)^2=10,x^2+(y+1)^2=5
Answer by ikleyn(52781) About Me  (Show Source):
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find the point of intersections of (x-1)^2+(y-3)^2=10,x^2+(y+1)^2=5
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You are given

%28x-1%29%5E2+%2B+%28y-3%29%5E2 = 10,
x%5E2+%2B+%28y%2B1%29%5E2 = 5.

It is the same as

x%5E2+-+2x+%2B+1+%2B+y%5E2+-6y+%2B+9 = 10,   (1)
x%5E2+%2B+y%5E2+%2B+2y+%2B+1 = 5.           (2)

Distract equation (2) from equation (1)  (both sides). You will get

-2x - 8y = -4,  or

x + 4y = 1.   (3)

From (3), express x = 1 - 4y and substitute it into either equation (1) or (2).
You will get single quadratic equation for one unknown y.

Solve it and get the answer.

See the lesson
    - Solving systems of algebraic equations of degree 2
on solving similar equations.

Also, you have this free online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.