Question

We are all too familiar with linear equations in two variables. These systems may have no solution, one solution, or infinitely many. Of course, we can interpret these solutions geometrically as two parallel lines, two intersecting lines, or two identical lines in the plane. How does this extend into linear equations in three variables? If a linear equation in two variables describes a line, what does a linear equation in three variables describe? Give a geometric interpretation for the possible solutions of a 3x3 linear system

Answer 1

Equation in three variable describes the equation of a plane in 3 dimensions.

It's equation is = aX + b.Y + c.Z = d

Where a ,b ,c,d are constants and are called direction cosines of a normal vector to the plane.

Like as line these system mau have no solution as if planes are parallel

If planes are intersecting then intersection point is a line

And if planes are coincidence then infinite no. Of solutions exist.

Geometrical interpretation of a 3 variable equation is a geometrical plane.

Plane is a surface having minimum two line containing in it.