Elimination Methods of Solving Linear System of Equations

The method of elimination is based on two facts:
(1) The solution of an equation is not changed if we multiply / divide both sides of the equation by the same constant factor.
eg. 2 x - 5 y = 10
same as 6 (2 x - 5 y) = 6 (10)
12 x - 30 y = 60

(2) The solution of an equation is not changed if we add / subtract equal quantities from both sides of an equation
eg. 2 x - 5 y = 10
same as 2 x - 5 y + (3 x - 2 y) = 10 + (3 x - 2 y)

(3) The system of equations is unchanged if we reorder the equations...
... so choose a convenient order...
                             3 x  - 6 y = 10
                                x + 3 y = -20
is same as:
                               x + 3 y = -20
                            3 x  - 6 y = 10

Example 1 - Elimination Methods of Solving Linear System of Equations

Example 2 - Elimination Methods of Solving Linear System of Equations 

Example 3 - Elimination Methods of Solving Linear System of Equations