1. Solve for the linear system: x−2y+3z=5 2x+y−4z=0 3x+4y−11z=−5 2. Ghana railways co−operation has 20 trains for it′s operations. It is observed that x trains can accommodate 2 passengers, y trains 3 passengers and z trains 5 passengers. Howeer, the totsl number of passrngers always present at Ghana railways are 64. During market day, 3 of x trains, 2 of y trains and 4 of z trains for a total of 10 trains were used. Determine the values of x, y and z.


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Question Number 186099 by akuba last updated on 01/Feb/23

$1 . S o l v e f o r t h e l i n e a r s y s t e m :$ $x - 2 y + 3 z = 5$ $2 x + y - 4 z = 0$ $3 x + 4 y - 11 z = - 5$ $2 . G h a n a r a i l w a y s c o - o p e r a t i o n h a s 20$ $t r a i n s f o r {i t}^{'} s o p e r a t i o n s . I t i s o b s e r v e d t h a t$ $x t r a i n s c a n a c c o m m o d a t e 2 p a s s e n g e r s,$ $y t r a i n s 3 p a s s e n g e r s a n d z t r a i n s 5$ $p a s s e n g e r s . H o w e e r, t h e t o t s l n u m b e r o f$ $p a s s r n g e r s a l w a y s p r e s e n t a t G h a n a$ $r a i l w a y s a r e 64 . D u r i n g m a r k e t d a y, 3 o f$ $x t r a i n s, 2 o f y t r a i n s a n d 4 o f z t r a i n s f o r$ $a t o t a l o f 10 t r a i n s w e r e u s e d . D e t e r m i n e$ $t h e v a l u e s o f x, y a n d z .$
	Answered by Mastermind last updated on 01/Feb/23

	$Ques . 1$ $x = 2, y = 0 and z = 1$ $solution$ $Using Row reduction Method$ $x - 2 y + 3 z = 5$ $5 y - 10 z = - 10$ $10 y - 20 z = - 20$ $x - 2 y + 3 z = 5 . . . . (1)$ $5 y - 10 z = - 10 . . . (2)$ $therefore, from (2), we have$ $y = 2 z - 2$ $putting y in (1), we get$ $x = z + 1$ $Now, z is a free variable$ $taking z as 1$ $we have x = 2, y = 0 and z = 1$ $Mastermind$
	Commented by akuba last updated on 01/Feb/23

	$p l e a s e e x p l a i n t h e r o w r e d u c t i o n m e t h o d$
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