# Service for Solving Linear Programming Problems

and other interesting typical problems
Русский

## Example №3. Solving of a System of Linear Equations by the Gauss elimination (No Solution)

This solution has been made using the calculator presented on the site.
Please note that the coefficients will disappear which located in the "red" positions. x1 - 2 x2 + 3 x3 - 4 x4 = 2 3 x1 + 3 x2 - 5 x3 + x4 = - 3 - 2 x1 + x2 + 2 x3 - 3 x4 = 5 3 x1 + 3 x3 - 10 x4 = 8
( 3 x1 + x1 * ( -3) )
+ ( 3 x2 + ( -2 x2) * ( -3) )
+ ( -5 x3 + 3 x3 * ( -3) )
+ ( x4 + ( -4 x4) * ( -3) )
= -3 + 2 * ( -3)
The "red" coefficient is zero. x1 - 2 x2 + 3 x3 - 4 x4 = 2 9 x2 - 14 x3 + 13 x4 = - 9 - 2 x1 + x2 + 2 x3 - 3 x4 = 5 3 x1 + 3 x3 - 10 x4 = 8
( -2 x1 + x1 * 2 )
+ ( x2 + ( -2 x2) * 2 )
+ ( 2 x3 + 3 x3 * 2 )
+ ( -3 x4 + ( -4 x4) * 2 )
= 5 + 2 * 2
The "red" coefficient is zero. x1 - 2 x2 + 3 x3 - 4 x4 = 2 9 x2 - 14 x3 + 13 x4 = - 9 - 3 x2 + 8 x3 - 11 x4 = 9 3 x1 + 3 x3 - 10 x4 = 8
( 3 x1 + x1 * ( -3) )
- 2 x2 * ( -3)
+ ( 3 x3 + 3 x3 * ( -3) )
+ ( -10 x4 + ( -4 x4) * ( -3) )
= 8 + 2 * ( -3)
The "red" coefficient is zero. x1 - 2 x2 + 3 x3 - 4 x4 = 2 9 x2 - 14 x3 + 13 x4 = - 9 - 3 x2 + 8 x3 - 11 x4 = 9 6 x2 - 6 x3 + 2 x4 = 2
The equation 3 and equation 2 are reversed. x1 - 2 x2 + 3 x3 - 4 x4 = 2 - 3 x2 + 8 x3 - 11 x4 = 9 9 x2 - 14 x3 + 13 x4 = - 9 6 x2 - 6 x3 + 2 x4 = 2
( 9 x2 + ( -3 x2) * 3 )
+ ( -14 x3 + 8 x3 * 3 )
+ ( 13 x4 + ( -11 x4) * 3 )
= -9 + 9 * 3
The "red" coefficient is zero. x1 - 2 x2 + 3 x3 - 4 x4 = 2 - 3 x2 + 8 x3 - 11 x4 = 9 10 x3 - 20 x4 = 18 6 x2 - 6 x3 + 2 x4 = 2
( 6 x2 + ( -3 x2) * 2 )
+ ( -6 x3 + 8 x3 * 2 )
+ ( 2 x4 + ( -11 x4) * 2 )
= 2 + 9 * 2
The "red" coefficient is zero. x1 - 2 x2 + 3 x3 - 4 x4 = 2 - 3 x2 + 8 x3 - 11 x4 = 9 10 x3 - 20 x4 = 18 10 x3 - 20 x4 = 20
( 10 x3 + 10 x3 * ( -1) )
+ ( -20 x4 + ( -20 x4) * ( -1) )
= 20 + 18 * ( -1)
The "red" coefficient is zero. x1 - 2 x2 + 3 x3 - 4 x4 = 2 - 3 x2 + 8 x3 - 11 x4 = 9 10 x3 - 20 x4 = 18 0 = 2
Equation 4 is false. The system has no solution.