Linear Equations in 3 Varibles

2x - 3y + 3z = -5 ------ (1)
3x + 2y - 5z = 34 ------ (2)
5x - 4y - 2z = 23 ------ (3)

5*(1) + 3*(2) :
19x - 9y = 77 ...... (4)

5*(3) - 2*(2) :
19x - 24y = 47 ...... (5)

(4) - (5) :
15y = 30
y = 2

Put y = 2 into (4):
19x - 9*2 = 77
19x - 18 = 77
19x = 95
x = 5

Put x = 5 and y = 2 into (1):
2*5 - 3*2 + 3z = -5
4 + 3z = -5
3z = -9
z = -3

Hence, x = 5, y = 2, z = -3.