How to solve linear relationships

Introduction:

      A linear relationship is the wing of linear algebra. A basic function of solving linear algebra is to find the solution of systems of linear equations in some unknowns with the help of known variables. Linear algebra has a demonstration in analytic geometry and the relationship is generalized in operator theory. Linear relationship associates with the families of vectors called vector spaces or linear spaces, and with functions contain one input vector and output vector, according to certain rules.

Example problems for solving linear relationships:

Example 1:

Solve the linear relationship in the equation.
     -3(-x - 6) = 3x - 23
Solution:
Given
-3(-x - 6) = 3x - 23
Multiply factors in left term
3x + 18 = 3x - 23
Subtract 18 to both sides
3x + 18 - 18 = 3x - 23 - 18
Grouping the above terms
3x = 3x - 41
Subtract 3x to both sides
3x - 3x = 3x - 41 -3x
By solving the above term

0x = -41

There is no real value for x, so the above equation has no solutions.