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

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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 )

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 $2x+5y=21,x+2y=8$

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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