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6. Cramer's Rule Method
Solve linear equations 12x+5y=7 and x+y=7 using Using Cramer's Rule Method

The equations can be expressed as
`12x+5y-7=0`

`x+y-7=0`

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

` D_x =|[5,-7],[1,-7]|`

` = 5 × -7 - -7 × 1`

` = -35 + 7`

` = -28`


` D_y =|[12,-7],[1,-7]|`

` = 12 × -7 - -7 × 1`

` = -84 + 7`

` = -77`


` D =|[12,5],[1,1]|`

` = 12 × 1 - 5 × 1`

` = 12-5`

` = 7`


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

`:. (x)/-28=(-y)/-77=(1)/7`

`:. (x)/-28=(1)/7,(-y)/-77=(1)/7`

`:. x=(-28)/(7),y=(77)/(7)`

`:. x=-4,y=11`

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