3x-2y-4z-2-3y-4z-2-2y-6z-1-

Question Number 6251 by net last updated on 20/Jun/16

3 x - 2 y - 4 z = 2

3 y - 4 z = - 2

2 y + 6 z = - 1

Answered by Rasheed Soomro last updated on 20/Jun/16

3 x - 2 y - 4 z = 2 \dots \dots \dots (i)

3 y - 4 z = - 2 \dots \dots \dots \dots . (i i)

2 y + 6 z = - 1 \dots \dots \dots \dots . (i i i)

2 \times (i i) : 6 y - 8 z = - 4 \dots \dots . (i v)

3 \times (i i i) : 6 y + 18 z = - 3 \dots \dots . (v)

(i v) - (v) : - 26 z = - 1 \Rightarrow z = \frac{1}{26}

S u b s t i t u t i n g z = \frac{1}{26} i n (i i)

3 y - 4 (\frac{1}{26}) = - 2 \Rightarrow 3 y = - 2 + \frac{2}{13} = - \frac{24}{13} \Rightarrow y = - \frac{24}{39}

S u b s t i t u t i n g v a l u e s o f y a n d z i n (i)

3 x - 2 (- \frac{24}{39}) - 4 (\frac{1}{26}) = 2

3 x + \frac{48}{39} - \frac{2}{13} = 2 \Rightarrow 117 x + 48 - 6 = 78

x = \frac{78 - 42}{117} = \frac{36}{117} = \frac{4}{13} \Rightarrow x = \frac{4}{13}