How do you determine the points of intersection for #x^2+y^2=1# and #y=x+1#?

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Answer 1 · 2016-11-20T04:44:58

We can substitute the second equation directly into the first.

#x^2 + (x + 1)^2 = 1#

#x^2 + x^2 + 2x + 1 = 1#

#2x^2 + 2x = 0#

#2x(x + 1) = 0#

#x =0 and -1#

#y = x + 1#

#y = 0 + 1 and y = -1 +1#

#y = 1 and y = 0#

The points of intersection are #(-1, 0)# and #(0, 1)#.

Hopefully this helps!