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`

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