where

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

So

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).