Find the points of intersections of these equations?
x^2+y^2=1
-x+y+1
This is what I've done so far, I isolated the y's out
y= +/- sqrt(1-x^2)
y=x+1
But I am stuck on how to make them together in order to find the point of intersection, any help is greatly appreciated!
do you mean
-x+y = 1 ????? so y=x+1
if so
circle with center at (0,0) and radius 1
line through (0,1) and (-1,0)
x^2 + (x+1)^2 = 1
x^2 + x^2 + 2 x + 1 = 1
2 x^2 + 2 x = 0
x(x+1) = 0
x = 0 or x = -1
line hits the circle at the x and y axis intersections
Thanks for the correction! I understand now
You are welcome.
To find the points of intersection between the equations x^2 + y^2 = 1 and -x + y + 1 = 0, you can follow these steps:
1. Start by substituting y from the second equation into the first equation.
-x + (y + 1) = 0
y = x - 1
2. Substitute this expression for y in the first equation:
x^2 + (x - 1)^2 = 1
3. Simplify and solve for x:
x^2 + (x^2 - 2x + 1) = 1
2x^2 - 2x = 0
2x(x - 1) = 0
This gives us two possible values for x:
x = 0 or x = 1
4. Substitute these x-values back into the second equation to find the corresponding y-values:
For x = 0:
-0 + y + 1 = 0
y = -1
For x = 1:
-1 + y + 1 = 0
y = 0
Therefore, the two points of intersection are (0, -1) and (1, 0).