Could there be a system of equations (one of them non-linear and the others linear) that has exactly three solutions? If so, how would you obtain one?

Question

anonymous · Answer

Is the attached what you mean?

The non-linear function is f(x) = x³ - 5x² + 10.
The linear function is g(x) = x / 2 + 1.

Three solutions, as required.

anonymous · Answer

No, what I mean is having a system of equations like the one below, but with three solutions:
3x-y+2z=1 (linear)
x+y=-1 (linear)
xy-z=0 (non-linear)

amistre64 · Answer

3x-y+2z=1
x+y=-1
xy-z=0

do some substitutions .... z = xy from the bottom, sub in the first

3x-y+2xy=1

y = -1-x from the second .... sub in the first

3x-(-1-x)+2x(-1-x)=1

expand and solve the quadratic ... then test