Question 972385
Find the point(s) of intersection of the line x - y = -6 and the circle x2 + y2 = 18 by solving the system of equations.
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solve by substitution:
x-y=6
y=x-6
..
x^2 + y^2 = 18 
x^2+(x-6)^2=18
x^2+x^2-12x+36=18
2x^2-12x+18=0
divide eq. by 2
x^2-6x+9=0 (perfect square)
(x-3)^2=0
(x-3)(x-3)=0
x=3 (multiplicity 2)
..
y^2=18-x^2
y^2=18-9=9
y=±√9=±3
y=3 (reject, does not check in first equation)
or 
y=-3
..
Point of intersection (3, -3)