Posted by **Kyle ** on Thursday, March 1, 2012 at 9:43am.

Solve the system

x^2+y^2-4x+2y=20

4x +3y =5

- math - Line+circle -
**MathMate**, Thursday, March 1, 2012 at 9:55am
Rewrite

x^2+y^2-4x+2y=20

as

(x-2)^2+(y+1)^2=25=5^2 ...(1)

represents a circle of radius 5 with centre (2,-1).

which intersects with the line

4x+3y=5 ...(2)

So write

y=(5-4x)/3 and substitute in the circle equation (1)

to get (x-2)^2+(((5-4x)/3)+1)^2=5^2

Solve for x in the above quadratic to get:

x=5 or x=-1

Find y accordingly.

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