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4x -9z =17 ------(1)
3x +y +15z =18 ------(2)
x+2y+3z=2 -----(3)

(1) : 4x -9z =17
=>x = (17 - 9z) / 4
Put x = (17 - 9z) / 4 into (3) ,
(17 - 9z) / 4 +2y 3z = 2
=> y = (-9 - 21z) / 8
Put x = (17 - 9z) / 4 & y = (-9 - 21z) / 8 into (2),
3[(17 - 9z) / 4] + (-9 - 21z) / 8 + 15z = 18
=>z = 1/3
Put z = 1/3 into x = (17 - 9z) / 4,
=> x = 5
Put z = 1/3 into y = (-9 - 21z) / 8,
=> y = -2