SOLUTION: Please help me solve this. I have tried several times but I am missing something or doing a step wrong. Please help me solve the determinants. 2x + 3y + z = 4 3x - z

Algebra ->  Systems-of-equations -> SOLUTION: Please help me solve this. I have tried several times but I am missing something or doing a step wrong. Please help me solve the determinants. 2x + 3y + z = 4 3x - z       Log On


   

Question 429060: Please help me solve this. I have tried several times but I am missing something or doing a step wrong.
Please help me solve the determinants.
2x + 3y + z = 4
3x - z = -3
x - 2y + 2z = -5
Found 2 solutions by Gogonati, mananth:
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:We rewrite the system:
system%28z=3x%2B3%2C+5x%2B3y=1%2C+7x-2y=-11%29The two last equations obtained a linear
system of two variables which we know to find its solutions.
system%285x%2B3y=1%2C7x-2y=-11%29,Its solution is: (-31/21,-134/63)
Substitute to find z=3x+3=3(-31/21)+3=-30/21
Answer:The solution is the ordered triple (-31/21, -134/63, -30/21).
Done.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2x+3y+1z=4--------------1
3x-z== -3--------------2
x-2y+2z=-5--------------3
consider equation 1 &2
2 x + 3 y + 1 z = 4
3 x + 0 y + -1 z = -3
Add the two
5x+3y= 1------------- 4
consider equation 2 & 3 Eliminate z
Multiply 2 by 2
we get
6x-2z=-6
x-2y+2z=-5
Add the two
7x-2y=-11-------------5 5
Consider (4) & (5)
Multiply 4 by 2
Multiply (5) by 3

Add the two
31x=-31 / 31
x= -1
Plug value of x in (2)
3x-1z=-3
-3-1z=-3
-1z=0
z=0
plug value of x & z in (1)
-2+3y=4
3y=6
y=2