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Home > Matrix & Vector calculators > Solving systems of linear equations using Gauss-Jordan Elimination method example
3. Gauss-Jordan Elimination method example ( Enter your problem )
( Enter your problem )
  1. Example `2x+5y=21,x+2y=8`
  2. Example `2x+5y=16,3x+y=11`
  3. Example `2x+3y-z=5,3x+2y+z=10,x-5y+3z=0`
  4. Example `x+y+z=3,2x-y-z=3,x-y+z=9`
 		Other related methods
  1. Inverse Matrix method
  2. Cramer's Rule method
  3. Gauss-Jordan Elimination method
  4. Gauss Elimination Back Substitution method
  5. Gauss Seidel method
  6. Gauss Jacobi method
  7. Elimination method
  8. LU decomposition using Gauss Elimination method
  9. LU decomposition using Doolittle's method
  10. LU decomposition using Crout's method
  11. Cholesky decomposition method
  12. SOR (Successive over-relaxation) method
  13. Relaxation method
2. Cramer's Rule method
(Previous method)		2. Example `2x+5y=16,3x+y=11`
(Next example)

1. Example `2x+5y=21,x+2y=8`


1. Solve Equations 2x+5y=21,x+2y=8 using Gauss-Jordan Elimination method

Solution:
Total Equations are `2`

`2x+5y=21 -> (1)`

`x+2y=8 -> (2)`

Converting given equations into matrix form
`2``5``21`
`1``2``8`


`R_1 larr R_1-:2`

 = 
 `1` `1=2-:2`
`R_1 larr R_1-:2`		 `5/2` `5/2=5-:2`
`R_1 larr R_1-:2`		 `21/2` `21/2=21-:2`
`R_1 larr R_1-:2`
`1``2``8`


`R_2 larr R_2- R_1`

 = 
`1``5/2``21/2`
 `0` `0=1-1`
`R_2 larr R_2- R_1`		 `-1/2` `-1/2=2-5/2`
`R_2 larr R_2- R_1`		 `-5/2` `-5/2=8-21/2`
`R_2 larr R_2- R_1`


`R_2 larr R_2xx-2`

 = 
`1``5/2``21/2`
 `0` `0=0xx-2`
`R_2 larr R_2xx-2`		 `1` `1=-1/2xx-2`
`R_2 larr R_2xx-2`		 `5` `5=-5/2xx-2`
`R_2 larr R_2xx-2`


`R_1 larr R_1-5/2xx R_2`

 = 
 `1` `1=1-5/2xx0`
`R_1 larr R_1-5/2xx R_2`		 `0` `0=5/2-5/2xx1`
`R_1 larr R_1-5/2xx R_2`		 `-2` `-2=21/2-5/2xx5`
`R_1 larr R_1-5/2xx R_2`
`0``1``5`


`i.e.`

`x=-2`

`y=5`

Solution By Gauss jordan elimination method.
`x = -2`

`y = 5`

This material is intended as a summary. Use your textbook for detail explanation.
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2. Cramer's Rule method
(Previous method)		2. Example `2x+5y=16,3x+y=11`
(Next example)


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