Sec1Sess13

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Linear system is a series of equations
variables are looked for that solve all equations

intersection points of the lines from functions from each equation represents solutions to the series of equations.

given 3 planes they could all intersect at one point and that point is the solution
Solution to AX=B is given by <math>X=A^{-1}B</math>

if in 3 planes if <math>plane_3</math> is parallel to <math>plane_1</math> and <math>plane_2</math> intersection, no solution could occur

if <math>plane_1</math> and <math>plane_2</math> intersection is within <math>plane_3</math> (<math>plane_3</math> contains intersection line) than infinitely many solutions could occur (any point on
the line is a solution)

if <math>plane_1</math>, <math>plane_2</math>, and <math>plane_3</math> are the same plane than the solution is that plane

An example of a case where 2 planes are parallel is when 2 of their 3 dimensions are always equal, e.g. x and y are equal but z is different.