Solve the following system of equations using Cramers rule. `5x-7y+z=11 ,6x-8y-z=15a n d3x+2y-6z=7`

Explanation

We have given:`5x-7y+z=11 ,6x-8y-z=15a n d3x+2y-6z=7`

As we know that the system of linear equation can be written in matrix form as `AX = B`

`implies A=|(5,-7,1),(6,-8,-1),(3,2,-6)|`,`X=[(x),(y),(z)]`,`B=[(11),(15),(7)]`

Now find the determinant of `A`,

`|A|= |(5,-7,1),(6,-8,-1),(3,2,-6)|`

`|A|=5[(– 8) (– 6) – (– 1) (2)] – 7[(– 6) (6) – 3(– 1)] + 1[2(6) – 3(– 8)]`

`|A|=250 – 231 + 36`

`|A|=Delta=55`

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