Answer:
x = -1 and y = -3.
y = -3 and z = -2.
Explanation:
xy+3x+2y=-6 ...... (1)
yz+y+3z=-3 ..........(2)
xz+2x+z=-2 ..........(3)
From the second equation:
yz + y = -3z - 3
y = (-3z - 3)/(z + 1)
Substitute for y in equation 1:
x(-3z - 3)/(z + 1) + 3x + 2(-3z - 3)/(z + 1) = -6
x(-3z - 3) + 3x(z + 1) + 2(-3x - 3) = -6(z + 1)
-3xz - 3x + 3xz + 3x - 6x - 6 = -6z - 6
-3xz + 3xz -6x + 6z = 0
- 6x + 6z = 0 ..........(4).
From the third equation:
xz + z = -2x - 2
z = (-2x - 2) / x + 1)
Now substitute for z in equation ( 4):
-6x + 6 (-2x - 2) / (x + 1) = 0
-6x(x + 1) - 12x - 12 = 0
-6x^2 - 18x - 12 = 0
x^2 + 3x + 2 = 0
(x + 2)(x + 1) = 0
x = -1, -2.
Substitute for x in equation 3:
-z - 2 + z = -2
-2 = -2
so we cant find z from this value of x.
When x = -2:
-2z - 4 + z = -2
-z = 2
z = -2.
Substitute for x = -1 in the first equation:
-y - 3 + 2y = -6
y = -6 + 3 = -3.
y= -3 and z = -2 satisfies equation 2.