How to find out how many solutions simultaneous equations have.

Hello, could anyone help me with this question?
How many solutions do these simultaneous equations have: y=x^3 and x-y=2.
I rearranged the second equation to get y=x-2 then said that x^3=x-2 to find where they intersect.
I then rearranged to get x^3-x+2=0 and tried to use factor theorem to find what x could be with no luck. Surely this would mean that they don't intersect but according to the answer book they intersect once. Could anyone help me please?
Am I supposed to actually draw the two equations on a graph as this may not be accurate?
Thanks

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Original post by etel

Hello, could anyone help me with this question?
How many solutions do these simultaneous equations have: y=x^3 and x-y=2.
I rearranged the second equation to get y=x-2 then said that x^3=x-2 to find where they intersect.
I then rearranged to get x^3-x+2=0 and tried to use factor theorem to find what x could be with no luck. Surely this would mean that they don't intersect but according to the answer book they intersect once. Could anyone help me please?
Am I supposed to actually draw the two equations on a graph as this may not be accurate?
Thanks