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

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Answer 1 · 2016-11-20T04:44:58

We can substitute the second equation directly into the first.

$x^{2} + {(x + 1)}^{2} = 1$ $x^2 + (x + 1)^2 = 1$

$x^{2} + x^{2} + 2 x + 1 = 1$ $x^2 + x^2 + 2x + 1 = 1$

$2 x^{2} + 2 x = 0$ $2x^2 + 2x = 0$

$2 x (x + 1) = 0$ $2x(x + 1) = 0$

$x = 0 and - 1$ $x =0 and -1$

$y = x + 1$ $y = x + 1$

$y = 0 + 1 and y = - 1 + 1$ $y = 0 + 1 and y = -1 +1$

$y = 1 and y = 0$ $y = 1 and y = 0$

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

Hopefully this helps!

How do you determine the points of intersection for x^2+y^2=1x2+y2=1x^2+y^2=1 and y=x+1y=x+1y=x+1?