Question

Given the system of equations

2x-3y-9z = 21
x+3z = -12
-3x+y-4z = 21

(a) determine whether the system is inconsistent or has infinitely many solutions;
Your answer is (input inconsistent or infinite)
(b) if your answer is "infinite" in (a), find the complete solution. Write x and y as functions of z.
x=
y=

Answer 1

2x - 3y - 9z = 21
-3x + y - 4z = 21--->(-3)
----------------
2x - 3y - 9z = 21
9x - 3y + 12z = - 63 -- result of multiplying by -3
---------------add
11x + 3z = - 42

x + 3z = -12 -->(-1)
11x + 3z = -42
--------------
-x - 3z = 12 -- result of multiplying by -1
11x + 3z = -42
-------------add
10x = - 30
x = -3

x + 3z = -12
-3 + 3z = -12
3z = -12 + 3
3z = -9
z = -3

2x - 3y - 9z = 21
2(-3) - 3y - 9(-3) = 21
-6 - 3y + 27 = 21
-3y + 21 = 21
-3y = 21 - 21
-3y = 0
y = 0

check...
-3x + y - 4z = 21 x + 3z = -12
-3(-3) + 0 - 4(-3) = 21 -3 + 3(-3) = -12
9 + 0 + 12 = 21 -3 - 9 = -12
21 = 21 (correct) -12 = -12 (correct)

x = -3, y = 0, z = -3


This system is consistent

Answer 2

@hartnn ....can you take a peak at this...it is not inconsistent or infinite.....I think it is consistent, but that does not seem to be an answer choice.

Answer 3

i am getting infinite solutions...

Answer 4

I even checked my solutions and they turned out correct

Answer 5

did I do something wrong and I am just missing it ??

Answer 6

checking your solution now..

Answer 7

the solution u got is one of the infinite solutions

Answer 8

Oh....I just thought my solutions were the only solutions

Answer 9

are you good with functions...because I am not and I cannot do the last part of the question

Answer 10

i can try