Solving systems of linear equations using Cramer's Rule method Example 2x+5y=16,3x+y=11

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Home > Matrix & Vector calculators > Solving systems of linear equations using Cramer's Rule method example

2. Cramer's Rule 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

1. Example `2x+5y=21,x+2y=8`
(Previous example)

3. Example `2x+3y-z=5,3x+2y+z=10,x-5y+3z=0`
(Next example)

2. Example `2x+5y=16,3x+y=11`

Solve Equations 2x+5y=16,3x+y=11 using Cramer's Rule method

Solution:
The equations can be expressed as
`2x+5y-16=0`

`3x+y-11=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`|D_x|`

	`5`	`-16`
	`1`	`-11`

`=5 × (-11) - (-16) × 1`

`=-55 +16`

`=-39`

`|D_y|`

	`2`	`-16`
	`3`	`-11`

`=2 × (-11) - (-16) × 3`

`=-22 +48`

`=26`

`|D|`

	`2`	`5`
	`3`	`1`

`=2 × 1 - 5 × 3`

`=2 -15`

`=-13`

`(x)/D_x=(-y)/D_y=(1)/D`

`:. (x)/-39=(-y)/26=(1)/-13`

`:. (x)/-39=(1)/-13,(-y)/26=(1)/-13`

`:. x=(-39)/(-13),y=(-26)/(-13)`

`:. x=3,y=2`

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