SOLUTION: My question is...solve for x, y, z. 2x+5y+z=22 3x-3y-z=-22 5x+y+2z=-3 I have... 2x+5y+z=22 -4x-10y-2z=44 45x+18y=0 3x-3y-z=-22 5x+ y+ 2z=-3 10x-18y=-4

Algebra ->  Systems-of-equations -> SOLUTION: My question is...solve for x, y, z. 2x+5y+z=22 3x-3y-z=-22 5x+y+2z=-3 I have... 2x+5y+z=22 -4x-10y-2z=44 45x+18y=0 3x-3y-z=-22 5x+ y+ 2z=-3 10x-18y=-4      Log On


   

Question 406673: My question is...solve for x, y, z.
2x+5y+z=22
3x-3y-z=-22
5x+y+2z=-3
I have...
2x+5y+z=22 -4x-10y-2z=44 45x+18y=0
3x-3y-z=-22 5x+ y+ 2z=-3 10x-18y=-41
___________ ____________ __________
5x+2y =0 5x-9y =41
I keep coming up with a fractionfor the last step.
Found 3 solutions by Alan3354, MathLover1, ewatrrr:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2x+5y+z=22
3x-3y-z=-22
5x+y+2z=-3
---------------
x = -2
y = 5
z = 1
Sometimes the answers are fractions. Not this time, tho.
================
I have...
-4x-10y-2z=44 45x+18y=0
5x+ y+ 2z=-3 10x-18y=-41
---------------
1x -9y = 41 *******************

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B5y%2Bz=22.................1.........solve for z and substitute in 2
3x-3y-z=-22..................2
5x%2By%2B2z=-3..................3


2x%2B5y%2Bz=22.................1
z=+-2x-5y+%2B+22

3x-3y-%28-2x-5y+%2B+22%29=-22..................2
3x-3y%2B2x%2B5y+-+22=-22
5x%2B2y+=-22%2B22
5x%2B2y+=+0................solve for y and substitute in 3

5x%2B2y+=+0
2y+=+-5x
y+=+-%285%2F2%29x
substitute y+=+-%285%2F2%29x in z=+-2x-5y+%2B+22
z=+-2x-5%28-%285%2F2%29x%29+%2B+22
z=+-2x%2B%2825%2F2%29x+%2B+22
z=+-2x%2B%2812.5%29x+%2B+22
z=+10.5x+%2B+22

5x%2By%2B2z=-3..................3 ..substitute z=+10.5x+%2B+22 and y+=+-%285%2F2%29x

5x%2B%28-%285%2F2%29x%29%2B2%2810.5x+%2B+22%29=-3..................3...calculate x

5x-%285%2F2%29x%2B21x+%2B44=-3
26x-2.5x+=-3-44
23.5x+=+-47
x+=+-47%2F23.5
x+=+-2

now find y and z

y+=+-%285%2F2%29x
y+=+-%285%2F2%29%28-2%29
y+=+-%285%2Fcross%282%29%29%28-cross%282%29%29
y+=+5


z=+10.5%28-2%29+%2B+22
z=+-21+%2B+22
z=+1
so, your answer is:
x+=+-2
y+=+5
z=+1
check:
2x%2B5y%2Bz=22.................1.
2%28-2%29%2B5%2A5%2B1=22
-4%2B25%2B1=22
-4%2B26=22
22=22

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

2x+5y+z=22

3x-3y-z=-22

5x+y+2z=-3



Solving by elimination 

2x+5y+z=22

3x-3y-z=-22

 5x + 2y = 0



6x-6y+2z=-44

5x+y+2z=-3

  11x - 5y = -47



 5x + 2y = 0

11x - 5y = -47



 25x + 10y = 0

 22x - 10y = -94

   47x = -94

     x = -2  and y = 5    ( 5x + 2y = 0, y = -5x/2= 10/2)

AND  z = 22-2x-5y = 1