SOLUTION: can someone help me? solve the system: { x+5y-z=4 {3x+4y+z=4 { x- y+z=0 I do not understand these questions. thanks for the help.

Algebra ->  Matrices-and-determiminant -> SOLUTION: can someone help me? solve the system: { x+5y-z=4 {3x+4y+z=4 { x- y+z=0 I do not understand these questions. thanks for the help.      Log On


   

Question 113455: can someone help me? solve the system:
{ x+5y-z=4
{3x+4y+z=4
{ x- y+z=0
I do not understand these questions. thanks for the help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There are 3 equations with 3 unknowns, so it should be possible
to find x, y, and z.
+x+%2B+5y+-+z+=+4
3x+%2B+4y+%2B+z+=+4
+x+-+y+%2B+z+=+0
----------------
add the 1st and 3rd
+x+%2B+5y+-+z+=4
+x-+y+%2B+z+=0
2x+%2B+4y+=+4
4y+=+4+-+2x
y+=+1+-+%281%2F2%29x
subtract this equation from the 2nd one
3x+%2B+4y+%2B+z+=4
2x+%2B+4y+=+4
x+%2B+z+=+0
z+=+-x
Now plug values for y and z into the 3rd equation
+x+-+y+%2B+z+=+0
x+-+%281+-+%281%2F2%29x%29+%2B+%28-x%29+=+0
x+-+1+%2B+%281%2F2%29x+-+x+=+0
%281%2F2%29x+=+1
x+=+2
z+=+-2
y+=+1+-+%281%2F2%29%2A2
y+=+0
The answers are
x = 2
y = 0
z = -2
----------
check answers
+x+%2B+5y+-+z+=+4
3x+%2B+4y+%2B+z+=+4
+x+-+y+%2B+z+=+0
-------------------
2+%2B+5%2A0+-+%28-2%29+=+4
2+%2B+2+=+4
-------------------
3%2A2+%2B+4%2A0+%2B+%28-2%29+=+4
6+-+2+=+4
------------------
2+-+0+%2B+%28-2%29+=+0
2+-+2+=+0
-------------------
OK