Example 1 - Elimination Methods of Solving Linear System of Equations

Example 1
Solve system of equations by elimination methods
                                           2 x  - 1 y = 2
                                           8 x + 2 y = 4

Solution
                                          2 x - 1 y = 2                                  (1)
                                          8 x + 2 y = 4                                 (2)
We can eliminate x or y
let's eliminate x:
                                         4  (2 x - 1 y = 2)                           (1)
                                          8 x + 2 y = 4                                (2)

                                            8 x - 4 y = 8                              (1')
                                            8 x + 2 y = 4                             (2')

Note:
a = b
c = d
\ a - c = b - d   or    a + c = b + d

(1') - (2'):
(8 x - 4 y) - (8 x + 2 y) = 8 - 4
0 x - 6 y = 4   (x has been eliminated)
 - 6 y = 4 
--> y = 4/(-6) = (-2)/3 » -0.67
\ y = -2/3  ----> (can sub. etc to find x ...)  x = 2/3 ...

solution is
x = 2/3 , y = -2/3
or (2/3 , -2/3)