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Example №5. Solving of a System of Linear Equations by the Gauss Jordan Elimination (Many Solutions)

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.
Знак системы2x1+3x2-x3+x4 = 1
8x1+12x2- 9 x3+8x4 = 3
4x1+6x2+3x3- 2 x4 = 3
2x1+3x2+9x3- 7 x4 = 3
The equation 1 multiplied by -4 is added to the equation 2.   more info
( 8 x1 + 2 x1 * ( -4) )
+ ( 12 x2 + 3 x2 * ( -4) )
+ ( -9 x3 + ( - x3) * ( -4) )
+ ( 8 x4 + x4 * ( -4) )
= 3 + 1 * ( -4)
The "red" coefficient is zero.
Знак системы2x1+3x2-x3+x4 = 1
- 5 x3+4x4 = - 1
4x1+6x2+3x3- 2 x4 = 3
2x1+3x2+9x3- 7 x4 = 3
The equation 1 multiplied by -2 is added to the equation 3.   more info
( 4 x1 + 2 x1 * ( -2) )
+ ( 6 x2 + 3 x2 * ( -2) )
+ ( 3 x3 + ( - x3) * ( -2) )
+ ( -2 x4 + x4 * ( -2) )
= 3 + 1 * ( -2)
The "red" coefficient is zero.
Знак системы2x1+3x2-x3+x4 = 1
- 5 x3+4x4 = - 1
5x3- 4 x4 = 1
2x1+3x2+9x3- 7 x4 = 3
The equation 1 multiplied by -1 is added to the equation 4.   more info
( 2 x1 + 2 x1 * ( -1) )
+ ( 3 x2 + 3 x2 * ( -1) )
+ ( 9 x3 + ( - x3) * ( -1) )
+ ( -7 x4 + x4 * ( -1) )
= 3 + 1 * ( -1)
The "red" coefficient is zero.
Знак системы2x1+3x2-x3+x4 = 1
- 5 x3+4x4 = - 1
5x3- 4 x4 = 1
10x3- 8 x4 = 2
The equation 2 is added to the equation 3.   more info
( 5 x3 + ( -5 x3) )
+ ( -4 x4 + 4 x4 )
= 1 + ( -1)
The "red" coefficient is zero.
Знак системы2x1+3x2-x3+x4 = 1
- 5 x3+4x4 = - 1
0 = 0
10x3- 8 x4 = 2
The equation 2 multiplied by 2 is added to the equation 4.   more info
( 10 x3 + ( -5 x3) * 2 )
+ ( -8 x4 + 4 x4 * 2 )
= 2 + ( -1) * 2
The "red" coefficient is zero.
Знак системы2x1+3x2-x3+x4 = 1
- 5 x3+4x4 = - 1
0 = 0
0 = 0
Знак системы2x1+3x2-x3+x4 = 1
- 5 x3+4x4 = - 1
The equation 2 is divided by -5.
Знак системы2x1+3x2-x3+x4 = 1
x3 - 4/5 x4 = 1/5
The equation 2 is added to the equation 1.   more info
2 x1
+ 3 x2
+ ( - x3 + x3 )
+ ( x4 + ( -4/5 x4) )
= 1 + 1/5
The "red" coefficient is zero.
Знак системы2x1+3x2+1/5x4 = 6/5
x3 - 4/5 x4 = 1/5
The equation 1 is divided by 2.
Знак системыx1 +3/2x2+1/10x4 = 3/5
x3 - 4/5 x4 = 1/5
Result:
x1 = 3/5 - 3/2 x2 - 1/10 x4
x3 = 1/5 + 4/5 x4








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