Solving systems of linear equations using Gauss-Jordan Elimination method Example 2x+5y=21,x+2y=8

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3. Gauss-Jordan Elimination method example ( Enter your problem )

( Enter your problem )

Example `2x+5y=21,x+2y=8`
Example `2x+5y=16,3x+y=11`
Example `2x+3y-z=5,3x+2y+z=10,x-5y+3z=0`
Example `x+y+z=3,2x-y-z=3,x-y+z=9`

Other related methods

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`

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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