linear and non-linear equations

Question

Explain why a system of linear equations cannot have exactly two solutions but a system of non-linear equations can. (Hint: you can use graphs to explain)...

 

Can someone help explain this to me please?

Answer 1

Linear equations are straight lines. A system only has three options: intersect in one point (because lines can't bend and turn around to cross each other again), never intersect (because they are parallel), or intersect in many points (because they lie on top of each other). 

Non-linear equations are graphs of parabolas, circles, ellipses, exponential equations, etc. Draw a two parabolas so they intersect twice, which would give you exactly two solutions.