A system of linear equations is given.2x -3x + 2y - 3z =x - 4y + 5z = -1y + z =1(a) Find the complete solution of the system, or show that there is no solution. (If there is no solution, enter NO SOLUTION. If the system is dependent, enter your answer in terms of t.)(х, у, 2) %3D(b) State whether the system is inconsistent, dependent, or neither.O inconsistentO dependentO neither

Answered: A system of linear equations is given.…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 4CC

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Question

A system of linear equations is given.
2x -
3x + 2y - 3z =
x - 4y + 5z = -1
y + z =
1
(a) Find the complete solution of the system, or show that there is no solution. (If there is no solution, enter NO SOLUTION. If the system is dependent, enter your answer in terms of t.)
(х, у, 2) %3D
(b) State whether the system is inconsistent, dependent, or neither.
O inconsistent
O dependent
O neither

Expert Solution

Step 1

Given linear equation is

$2 x - y + z = 0 3 x + 2 y - 3 z = 1 x - 4 y + 5 z = - 1$

Step 2

Now (a)

$2 x - y + z = 0 . . . . (1) 3 x + 2 y - 3 z = 1 . . . . (2) x - 4 y + 5 z = - 1 . . . . (3) s o l v e e q u a t i o n (1), (2) a n d (3) 2 x - y + z = 0 x = \frac{y - z}{2} p u t t h e v a l u e x = \frac{y - z}{2} i n (2) e q u a t i o n 3 (\frac{y - z}{2}) + 2 y - 3 z = 1 3 y - 3 z + 4 y - 6 z = 2 7 y - 9 z = 2 y = \frac{2 + 9 z}{7} N o w x = \frac{\frac{2 + 9 z}{7} - z}{2} x = \frac{2 + 9 z - 7 z}{14} x = \frac{2 + 2 z}{14} x = \frac{1 + z}{7} S o x = \frac{1 + z}{7}, y = \frac{2 + 9 z}{7} P u t t h e v a l u e o f x a n d y i n a n y a b o v e e q u a t i o n (1), (2) a n d (3) \frac{1 + z}{7} - 4 (\frac{2 + 9 z}{7}) + 5 z = - 1 1 + z - 8 - 36 z + 35 z = - 7 0 = 0 T h u s t h e r e i s i n f i n i t l y m a n y s o l u t i o n .$

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