2xy-x-y-i-6xz-6z-2x-ii-3yz-3y-4z-iii-Solve-for-x-y-and-z-

Question Number 9449 by tawakalitu last updated on 08/Dec/16

2 xy = x + y \dots \dots (i)

6 xz = 6 z - 2 x \dots . . (ii)

3 yz = 3 y + 4 z \dots \dots . (iii)

Solve for x, y and z

Answered by mrW last updated on 09/Dec/16

(i) \Rightarrow (2 x - 1) y = x

y = \frac{x}{2 x - 1} \dots . (iv)

(ii) \Rightarrow 3 (x - 1) z = - x

z = \frac{- x}{3 (x - 1)} \dots . (v)

(iii) \Rightarrow - \frac{{3 x}^{2}}{3 (x - 1) (2 x - 1)} = \frac{3 x}{2 x - 1} - \frac{4 x}{3 (x - 1)}

- {3 x}^{2} = 9 x (x - 1) - 4 x (2 x - 1)

- {3 x}^{2} = {9 x}^{2} - 9 x - {8 x}^{2} + 4 x

{4 x}^{2} - 5 x = 0

x (x - \frac{5}{4}) = 0

x_{1} = 0

x_{2} = \frac{5}{4}

y_{1} = \frac{0}{2 \times 0 - 1} = 0

y_{2} = \frac{5}{4 \times (2 \times \frac{5}{4} - 1)} = \frac{5}{6}

z_{1} = - \frac{0}{3 \times (0 - 1)} = 0

z_{2} = - \frac{5}{4 \times 3 \times (\frac{5}{4} - 1)} = - \frac{5}{3}

(x, y, z) = (0, 0, 0) or (\frac{5}{4}, \frac{5}{6}, - \frac{5}{3})

Commented by tawakalitu last updated on 08/Dec/16

i really appreciate sir . God bless you .