Answer
$(-1,0),(0,1)$
Work Step by Step
$x^2+y^2=1$
$-x+y=1$
Rewrite second equation in slope-intercept form:
$y=x+1$
Substitute $y$ in the first equation:
$x^2+(x+1)^2=1$
Solve for $x$:
$x^2+x^2+2x+1=1$
$2x^2+2x=0$
$2x(x+1)=0$
$x=-1,0$
Substitute for $x=-1$ in the second equation:
$1+y=1$
$y=0$
Substitute for $x=0$ in the second equation:
$0+y=1$
$y=1$
The points of intersection are $(-1,0),(0,1)$
