2x + 3y -  z = 1

 x -  y -  z = 2

3x + 2y - 3z = 3

`

Get it in echelon form

`

Ax + By + Cz = D

     Ey + Fz = G

          Hz = I

`

2x + 3y -  z = 1

 x -  y -  z = 2

3x + 2y - 3z = 3

`

Get rid of the x in the 2nd equation by multiplying it by -2,

getting -2x + 2y + 2z = -4, and adding 1 times the first equation to it,

getting  5y + z = -3.  Replace the second equation with this one

`

2x + 3y -  z =  1

     5y +  z - -3 

3x + 2y - 3z =  3

`

Get rid of the 3x in the 3rd equation by multiplying it by 2,

getting 6x + 4y - 6z = 6, and adding -3 times the first equation to it,

namely -6x - 9y + 3z = -3, getting  -5y - 3z = 3.  Replace the third equation

with this one

`

2x + 3y -  z =  1

     5y +  z = -3 

    -5y - 3z =  3

`

Get rid of the -5y in the 3rd equation by multiplying it by 1,

and adding 1 times the second equation to it, getting  -2z = 0

Replace the third equation with this one

`

2x + 3y -  z =  1

     5y +  z = -3 

         -2z =  0

`

Finish by:

(1) solving the third equation for z

(2) Substitute the value you got for z into the second equation, and 

solve for y   

(3) Substitute the values of z and y into the first equation and solve 

for x.  Answer (x, y, z) = (7/5, -3/5, 0)



Edwin 

 

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