Question

How many solutions does a system of linear equations in three variables have? Can systems of linear equations have infinitely many solutions? Under what circumstances could that occur?

Answer 1

A system of linear equations in three variables can have a unique solution, no solution, or infinitely many solutions; just like linear equations in two variables. The circumstances under which infinitely many solutions can occur are when three planes intersect in a line or all three planes happen to be the same plane.

Answer 2

Oh thank you!

Answer 3

You rock branlegr!