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Find the points of intersection, if any, of the pair of curves :
x^2+y^2=13 , y=x+1
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Substitute y from the second equation into the first one. In this way you exclude y and obtain single equation for variable x:
+ = .
Simplify and solve this quadratic equation:
= ,
= .
The roots are = -3 and = 2.
Hence, the pairs (x,y) = (-3,-2) and (2,3) are our intersection points.
Answer. the pairs (x,y) = (-3,-2) and (2,3) are the two intersection points.