SOLUTION: how can i do this: x-y+z=0 3x-2y+6z=9 -x+y-2z=21

Algebra ->  Expressions-with-variables -> SOLUTION: how can i do this: x-y+z=0 3x-2y+6z=9 -x+y-2z=21      Log On


   

Question 117577This question is from textbook
: how can i do this:
x-y+z=0
3x-2y+6z=9
-x+y-2z=21 This question is from textbook

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x-y%2Bz=0………(1)
3x-2y%2B6z=9……………..(2)
-x%2By-2z=21…………..(3)

In order to solve this system for x, y, and z, first you need to eliminate one unknown variable. If you look at (1) and (3) you will see that x and y have opposite signs and same coefficient which is 1; so, we can add these and eliminate x and y and find out what z is.
x-y%2Bz=0………(1)

+-x%2By-2z=21…………..(3)
------------------------------
x+%2B%28-x%29-y+%2B+y+%2B+z+%2B+%28-2z%29=+0+%2B+21……….cancel x and y
z-2z=21
-z+=+21………multiply both sides by -1
z+=+-+21……………………solution #1
Now plug in solution #1 in equation (1) , (2), or (3). I will choose equation (1) and multiply it by 3, then subtract (2) from (1) to find out what y is.
x-y%2Bz=0………multiply both sides by 3………….(1)
3x-2y%2B6z=9……………..(2)
--------------------------------------------
3x-3y%2B3z=0………………….(1)………. subtract (2) from (1)
-3x-2y%2B6z=9……………..(2)
---------------------------------------------
3x-3x-3y-%28-2y%29%2B3%28-21%29-6%28-21%29=0-9……

-3y%2B2y-63%2B126=-9……
-y%2B63=-9……
-y=-9-63……
-y=-72……multiply both sides by -1

y=72……solution #2
Now choose either one of the three equations, plug in values for y and z and find out what x is.
x-y%2Bz=0…………………………….(1)

x=y-z……
x=72-%28-21%29……
x=72%2B21……
x+=+93
Check:
x-y+%2Bz+=0……..............(1)
93-72+%2B%28-21%29+=0……
93-72-21=0……
93-93=0……
0+=+0
3x-2y+%2B6z+=9……..............(2)
3%2893%29-2%2872%29+%2B6%28-21%29+=9
279-144-126+=9
279-270+=9
9++=+9
Check …(3)… by yourself