2x + z = -1 + y --- (1)
8x - 3y = 3 --- (2)
6x - 2y + 3z = 0 --- (3)
From (2), we have:
3y = 8x - 3
y = (8/3)x - 1 --- (4)
Substituting (4) into (1), we will get:
2x + z = -1 + ((8/3)x - 1)
2x + z = -2 + (8/3)x
z = -2 + (2/3)x --- (5)
Substituting (4) and (5) into (3), we will get:
6x - 2((8/3)x - 1) + 3(-2 + (2/3)x) = 0
6x - (16/3)x + 2 - 6 + 2x = 0
(8/3)x - 4 = 0
(8/3)x = 4
(2/3)x = 1
x = 3/2
Substituting x = 3/2 into (4), we will get:
y = (8/3)(3/2) - 1
y = 4 - 1
y = 3
Substituting x = 3/2 into (5), we will get:
z = -2 + (2/3)(3/2)
z = -2 + 1
z = -1
Hence, x = 3/2, y = 3 and z = -1