SOLUTION: How do I solve: y=x^3-2x^2+x-1 y=-x^2+3x-1 I substituted y=-x^2+3x-1 -x^2+3x-1=x^3-2x^2+x-1 0=x^3-x^2-2x Not sure what to do next

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: How do I solve: y=x^3-2x^2+x-1 y=-x^2+3x-1 I substituted y=-x^2+3x-1 -x^2+3x-1=x^3-2x^2+x-1 0=x^3-x^2-2x Not sure what to do next      Log On


   

Question 568770: How do I solve:
y=x^3-2x^2+x-1
y=-x^2+3x-1
I substituted y=-x^2+3x-1 -x^2+3x-1=x^3-2x^2+x-1
0=x^3-x^2-2x
Not sure what to do next
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+x%5E3+-+2x%5E2+%2B+x+-+1+
+y+=+-x%5E2+%2B+3x+-+1+
By substitution:
+x%5E3+-+2x%5E2+%2B+x+-+1+=+-x%5E2+%2B+3x+-+1+
Add 1 to both sides
+x%5E3+-+2x%5E2+%2B+x++=+-x%5E2+%2B+3x++
+x%5E3+-+x%5E2+-+2x+=+0+
Factor out +x+
+x%2A%28+x%5E2+-+x+-+2+%29+
The solutions are:
+x+=+0+
+x%5E2+-+x+-+2+=+0+
+%28+x+-+2+%29%2A%28+x+%2B+1+%29+=+0+
+x+=+2+
+x+=+-1+
You can verify these by plugging them
back into +x%5E3+-+x%5E2+-+2x+=+0+