Example 2 - Elimination Methods of Solving Linear System of Equations

Example 2
Solve system of equations by elimination methods
3 x - 4 y = 5
2 x - 6 y = 10

Solution
3 x - 4 y = 5                                                                                                   (1)
2 x - 6 y = 10                                                                                                 (2)
eliminate y:
(3 x - 4 y = 5)     . 3                                                                                       (1)
(2 x - 6 y = 10 )  . 2                                                                                       (2)

9 x - 12 y = 15                                                                                              (1')
4 x - 12 y = 20                                                                                              (2')

(2') - (1'):
(4 x - 12 y) - (9 x - 12 y) = 20 - 15
0 y - 5 x = 5   (y has been eliminated)
- 5 x = 5 
\ x = 5/(-5)  ==> x = -1
find "y" by back sub...
from (1): 3 (-1)  - 4 y = 5
\ -4 y = 8 ==> y = -2

\ solution is
x = -1 , y = -2
or (-1 , -2)