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

Nov 20, 2016

We can substitute the second equation directly into the first.

${x}^{2} + {\left(x + 1\right)}^{2} = 1$

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

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

$2 x \left(x + 1\right) = 0$

$x = 0 \mathmr{and} - 1$

$y = x + 1$

$y = 0 + 1 \mathmr{and} y = - 1 + 1$

$y = 1 \mathmr{and} y = 0$

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

Hopefully this helps!