F3 Algebra <急>

2x + y - z = 4.5 …… (1)
x + 2y + z = 1.5 …… (2)
2(x² + y² + z²) = 13 ….. (3)

(1) + (2):
3x + 3y = 6²²
x = 2 - y …… (4)

(2)*2 - (1):
3y + 3z = -1.5
z = -0.5 - y …… (5)

Put (4) and (5) into (3):
2[(2 - y)² + y² + (-0.5 - y)²] = 13
2(4 - 4y + y² + y² + 0.25 + y + y²) = 13
6y² - 6y + 8.5 = 13
12y² - 12y - 9 = 0
4y² - 4y - 3 = 0
(2y - 3)(2y + 1) = 0
2y = 3 or 2y = -1
y = 1.5 or y = -0.5

When y = 1.5:
(4):
x = 2 - 1.5
x = 0.5
(5):
z = -0.5 - 1.5
z = -2

When y = -0.5:
(4):
x = 2 - (-0.5)
x = 2.5
(5):
z = -0.5 - (-0.5)
z = 0

Hence, x = 0.5, y = 1.5, z = -2
or x = 2.5, y = -0.5, z = 0