## xy+3x+2y=-6 yz+y+3z=-3 xz+2x+z=-2 Find x, y and z ​

Question

xy+3x+2y=-6
yz+y+3z=-3
xz+2x+z=-2
Find x, y and z

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1 week 2021-11-20T20:20:31+00:00 1 Answer 0 views 0

x = -1 and y = -3.

y = -3 and z = -2.

Step-by-step 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.