Solving systems of linear equations using Cramer's Rule method Example 2x+5y=21,x+2y=8

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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. Inverse Matrix 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 Cramer's Rule method

Solution:
The equations can be expressed as
`2x+5y-21=0`

`x+2y-8=0`

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

`|D_x|`

	`5`	`-21`
	`2`	`-8`

`=5 × (-8) - (-21) × 2`

`=-40 +42`

`=2`

`|D_y|`

	`2`	`-21`
	`1`	`-8`

`=2 × (-8) - (-21) × 1`

`=-16 +21`

`=5`

`|D|`

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

`=2 × 2 - 5 × 1`

`=4 -5`

`=-1`

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

`:. (x)/2=(-y)/5=(1)/-1`

`:. (x)/2=(1)/-1,(-y)/5=(1)/-1`

`:. x=(2)/(-1),y=(-5)/(-1)`

`:. x=-2,y=5`

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