Question

Solve 3x + 2y – z = 1
x – 2y + z = 0
2x + y – 3z = -1

Answer 1

3x+2y-z=1

x-2y+z=0

add them,

4x=1 => x=1/4

substitute x in the first equation with the new found value of x.

what we get , 2y-z= 1- 3*1/4 = 1 - 3/4 = 1/4

also substitute x with 1/4 in the third equation also which is , 2x+y-3z = -1, putting x=1/4 here we get,

y - 3z = -1 -2*1/4 = -1 -1/2 = -3/2

so we have y-3z = -3/2

and2y - z = 1/4

multiplying the first equation with -2 we get , -2y + 6z = 3

now adding this with the second equation we get, -2y + 6z + 2y - z = 3 + 1/4 => 5z= 13/4 => z=13/20

Using x=1/4 and z=13/20 in any one of the equation we get, y=9/20

so the answers are ,

x=1/4

y=9/20

z=13/20

Answer 2

{3 x+2 y = z+1, x+z = 2 y, 2 x+y+1 = 3 z}

{z = 3 x+2 y-1, z = 2 y-x, z = (2 x)/3+y/3+1/3}

x = 1/4, y = 9/20, z = 13/20