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

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

Answers ( )

    0
    2021-11-20T20:22:25+00:00

    Answer:

    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.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )