`x=| (4,3,1),(10,-6,-3),(4,-9,3) |/Delta`

`y=| (1,4,1),(2,10,-3),(4,4,3) |/Delta`

where

`Delta=| (1,3,1),(2,-6,-3),(4,-9,3) |`

= 1(−45) − 2(18) + 4(−3)

= −93

Note: Once we have x and y, we can find z without using Cramer's Rule.

So

`x=(4(-45)-10(18)+4(-3))/-93` `=(-372)/-93` `=4`

`y=(1(42)-2(8)+4(-22))/-93` `=(-62)/-93` `=2/3`

Using these two results, we can easily find that z = -2.

Checking the solution:

[1] `(4) + 3(2/3) + -2 = 4`

[2] `2(4) - 6(2/3) - 3(-2) = 10`

[3] `4(4) - 9(2/3) + 3(-2) = 4`

So the solution is `(4, 2/3, -2)`.

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