Can someone help me understand whats the difference between

Can someone help me understand what\'s the difference between trivial and nontrivial solutions

like for this question:

I got the answer a= +/- 2 by the substitution method and i don\'t understand what makes it a nontrivial solution. How would I answer it if it asked trivial solutions?

Solution

yes, you got a right answer.

if a=+/- 2, then system has nontrivial solution,

because when a=+/ -2, both equation are identical.

So, it has many solutions.

trivial solutions: there are one solution exists x=0, y=0