SOLUTION: 4. Solve x + y - z = 0 2x - y + z = 6 -x + y + z = 8 Show your answers as (x,y,z) PLEASE SHOW ALL WORK THANK YOU

Algebra ->  Graphs -> SOLUTION: 4. Solve x + y - z = 0 2x - y + z = 6 -x + y + z = 8 Show your answers as (x,y,z) PLEASE SHOW ALL WORK THANK YOU       Log On


   

Question 118915: 4. Solve
x + y - z = 0
2x - y + z = 6
-x + y + z = 8
Show your answers as (x,y,z)
PLEASE SHOW ALL WORK
THANK YOU
Found 2 solutions by mayank, MathLover1:
Answer by mayank(15) About Me  (Show Source):
You can put this solution on YOUR website!
let x+y-z=0 ---1
and 2x-y+z=6 ---2
and -x+y+z=8 ---3
now adding 1 and 3 gives 2y=8
thus y=4 ---4
putting value of y in eq 1 gives x+4-z=0
thus x-z=-4-----5
now putting value of y in eq 2 gives 2x-4+z=6
thus 2x+z=10---6
Adding eq 5 and 6 we get,
3x=6
thus x=2 ----7
putting values of x and y in eq 1 gives 2+4-z=0
thus 6-z=0
thus z=6-----8
thus from eq 4,7 and 8 we get x,y,z as 2,4 and 6 respectively

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+y+-+z+=+0+…………….(1)
2x+-+y+%2B+z+=+6+…………..(2)
-x+%2B+y+%2B+z+=+8………………(3)

Take (1) and (3), add them to eliminate x and z and find y

cross%28x+%29%2B+y+cross%28-+z%29+=+0+…………….(1)
+cross%28-x+%29%2B+y+%2Bcross%28+z%29+=+8………………(3)
----------------------------
2y+=+8
y+=+4
take
x+%2B+y+-+z+=+0+…………….(1)….plug in y
x+%2B+4+-+z+=+0+…………
x++-+z+=+-4+………
x+=+z+-+4+…………….(a)

Take 2x+-+y+%2B+z+=+6+…………..(2) and plug in x and y to find z

+2%28z+-4+%29+-+4+%2B+z+=+6…………….
+2z+-8+-+4+%2B+z+=+6…………….
+3z+-12+=+6…………….divide both sides by 3
+z+-4+=+2…………….

+z+=+2%2B4+…………….
+z+=+6+…………….

Now find x

x+=+z+-+4+…………….(a)
x+=+6+-+4+……
x+=+2+……

Check:
x+=+2+……
y+=+4
+z+=+6+…………….
plug in values for x,y, and z

x+%2B+y+-+z+=+0+…………….(1)
2+%2B+4+-+6+=+0+…………….
6+-+6+=+0+…………….
0+=+0+…………….

2x+-+y+%2B+z+=+6+…………..(2)
2%2A2+-+4+%2B+6+=+6+…………..
4+-+4+%2B+6+=+6+…………..
6+=+6+…………..

-x+%2B+y+%2B+z+=+8………………(3)
-2+%2B+4%2B+6+=+8…………
2%2B+6+=+8…………
8+=+8……………