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

This solution was made using the calculator presented on the site.
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Please note that the coefficients will disappear which located in the "red" positions.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
3x1+3x2- 5 x3+x4 = - 3
- 2 x1+x2+2x3- 3 x4 = 5
3x1+3x3- 10 x4 = 8
The equation 1 multiplied by -3 is added to the equation 2.   more info
( 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.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
9x2- 14 x3+13x4 = - 9
- 2 x1+x2+2x3- 3 x4 = 5
3x1+3x3- 10 x4 = 8
The equation 1 multiplied by 2 is added to the equation 3.   more info
( -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.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
9x2- 14 x3+13x4 = - 9
- 3 x2+8x3- 11 x4 = 9
3x1+3x3- 10 x4 = 8
The equation 1 multiplied by -3 is added to the equation 4.   more info
( 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.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
9x2- 14 x3+13x4 = - 9
- 3 x2+8x3- 11 x4 = 9
6x2- 6 x3+2x4 = 2
The equation 3 and equation 2 are reversed.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
- 3 x2+8x3- 11 x4 = 9
9x2- 14 x3+13x4 = - 9
6x2- 6 x3+2x4 = 2
The equation 2 multiplied by 3 is added to the equation 3.   more info
( 9 x2 + ( -3 x2) * 3 )
+ ( -14 x3 + 8 x3 * 3 )
+ ( 13 x4 + ( -11 x4) * 3 )
= -9 + 9 * 3
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
- 3 x2+8x3- 11 x4 = 9
10x3- 20 x4 = 18
6x2- 6 x3+2x4 = 2
The equation 2 multiplied by 2 is added to the equation 4.   more info
( 6 x2 + ( -3 x2) * 2 )
+ ( -6 x3 + 8 x3 * 2 )
+ ( 2 x4 + ( -11 x4) * 2 )
= 2 + 9 * 2
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
- 3 x2+8x3- 11 x4 = 9
10x3- 20 x4 = 18
10x3- 20 x4 = 20
The equation 3 multiplied by -1 is added to the equation 4.   more info
( 10 x3 + 10 x3 * ( -1) )
+ ( -20 x4 + ( -20 x4) * ( -1) )
= 20 + 18 * ( -1)
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
- 3 x2+8x3- 11 x4 = 9
10x3- 20 x4 = 18
0 = 2
Equation 4 is false. The system has no solution.

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