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

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Home > Matrix & Vector calculators > Solving systems of linear equations using Gauss Elimination Back Substitution method example

4. Gauss Elimination Back Substitution 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

3. Gauss-Jordan Elimination 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 Elimination Back Substitution 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_2 larr R_2-1/2xx R_1`

	`2`	`5`		`21`
	`0` `0=1-1/2xx2` `R_2 larr R_2-1/2xx R_1`	`-1/2` `-1/2=2-1/2xx5` `R_2 larr R_2-1/2xx R_1`		`-5/2` `-5/2=8-1/2xx21` `R_2 larr R_2-1/2xx R_1`

`i.e.`

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

`-1/2y=-5/2 ->(2)`

Now use back substitution method
From (2)
`-1/2y=-5/2`

`=>y=-5/2xx-2=5`

From (1)
`2x+5y=21`

`=>2x+5(5)=21`

`=>2x+25=21`

`=>2x=21-25=-4`

`=>x=(-4)/(2)=-2`

Solution using back substitution method.
`x = -2`

`y = 5`

This material is intended as a summary. Use your textbook for detail explanation.
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