SOLUTION: Solve the System By Substitution - x - y - z = - 8 -4x + 4y + 5z = 7 2x + 2z = 4 A step-by-step explanation would be greatly appreciated. Thank you :)

Algebra ->  Equations -> SOLUTION: Solve the System By Substitution - x - y - z = - 8 -4x + 4y + 5z = 7 2x + 2z = 4 A step-by-step explanation would be greatly appreciated. Thank you :)       Log On


   

Question 1101285: Solve the System By Substitution
- x - y - z = - 8
-4x + 4y + 5z = 7
2x + 2z = 4
A step-by-step explanation would be greatly appreciated. Thank you :)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

system%28-x+-+y+-+z+=+-+8%2C-4x+%2B+4y+%2B+5z+=+7%2C2x+%2B+2z+=+4%29

Solve 2x+%2B+2z+=+4 for x
      2x+=+4-2z
      x+=+2-z

Substitute 2-z for x in -x+-+y+-+z+=+-8
                        -%282-z%29+-+y+-+z+=+-8
                        -2%2Bz-y-z+=+-8 
                        -2-y+=+-8  
                        -y+=+-6
                        y+=+6

Substitute 2-z for x and 6 for y in the only equation
we haven't used, which is  -4x+%2B+4y+%2B+5z+=+7
                           -4%282-z%29+%2B+4%286%29+%2B+5z+=+7
                           -8%2B4z+%2B+24+%2B+5z+=+7
                           9z+%2B+16+=+7
                           9z+=+-9
                           z+=+-1

Finally find x by substituting -1 for z in x+=+2-z
                                           x+=+2-%28-1%29 
                                           x=2%2B1
                                           x=3 

          (x,y,z) = (3,6,-1)

Edwin