Solve Equations 2x+5y=16,3x+y=11 using Gauss Elimination Back Substitution method

Solution:
Total Equations are `2`

`2x+5y=16 -> (1)`

`3x+y=11 -> (2)`

Converting given equations into matrix form

	`2`	`5`		`16`
	`3`	`1`		`11`

`R_2 larr R_2-3/2xx R_1`

=	`2` `5` `16`  `0` `0=3-3/2xx2` `R_2 larr R_2-3/2xx R_1`  `-13/2` `-13/2=1-3/2xx5` `R_2 larr R_2-3/2xx R_1`  `-13` `-13=11-3/2xx16` `R_2 larr R_2-3/2xx R_1`

`i.e.`

`2x+5y=16 ->(1)`

`-13/2y=-13 ->(2)`

Now use back substitution method
From (2)
`-13/2y=-13`

`=>y=-13xx-2/13=2`

From (1)
`2x+5y=16`

`=>2x+5(2)=16`

`=>2x+10=16`

`=>2x=16-10=6`

`=>x=(6)/(2)=3`

Solution using back substitution method.
`x = 3`

`y = 2`

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