Question 1009151
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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:

{{{x^2}}} + {{{(x+1)^2}}} = {{{13}}}.

Simplify and solve this quadratic equation:

{{{2x^2 + 2x - 12}}} = {{{0}}},

{{{x^2 + x - 6}}} = {{{0}}}.

The roots are {{{x[1]}}} = -3 and {{{x[2]}}} = 2.

Hence, the pairs (x,y) = (-3,-2) and (2,3) are our intersection points.

<U>Answer</U>. the pairs (x,y) = (-3,-2) and (2,3) are the two intersection points.
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