IMMEDIATE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Solve by elimination:

x + y + z  =  10

-x + y - z  =  0

-x + z  =  1

 

Combine the first two equations by addition (adding down the columns):

     x + y + z  =  10

    -x + y - z  =    0

    --------------------

         2y       =  10     --->     y  =  5

 

Replace y with 5 in the first equation:    

     x + y + z  =  10     --->      x + 5 + z  =  10     --->     x + z  =  5

 

Combine this equation with the third of the original equations by addition:

     x + z  =  5

   -x + z  =   1

   ---------------

         2z  =   6

           z  =  3

 

Since  y = 5  and  z = 5.5,  substitute these values into the first equation:

     x + y + z  =  10     --->      x + 5 + 3 =  10     --->     x + 8  =  10     --->      x  =  2

Solve by substitution:

By considering the 3rd equation,

z=1+x

By considering the 2nd equation,

y=x+z=x+1+x=2x+1

Substitute these into the 1st equation,

x+(2x+1)+(1+x)=10

4x+2=10

2x+1=5

x=2

y = 2(2)+1 = 5

z = 1+(2) = 3

 

I love substitution method more, it's faster.