Question

Solve for x,y, and z:

3x - y + z = -3
-2x + y - 2z = 8
-4XL + 3y - z = 6

Answer 1

The value of x=1; y=2; z=-4

Solution:

As given in the problem,

`3x - y + z = -3`

`=> y = 3x +z+3` -----(i)

`-2x + y - 2z = 8`

`=> y =2x +2z +8` ----- (ii)

So From (i) and (ii) we get,

`3x +z+3 = 2x +2z +8`

`=> 3x + z +3 -2x- 2z -8 =0`

`=> x -z -5 =0`

`=> z= x-5` -----------(iii)

Now,
`-4x + 3y - z = 6`

`=> -4x + 3(3x+z+3) - z =6` (// substituting value of y from (i))

`=> -4x +3(3x+x-5+3)-(x-5) = 6` (//substituting value of z from (iii))

`=> -4x + 12x -6 -x +5 =6`

`=> 7x -1 =6`

`=> 7x = 7`

`=> x = 1`

So from (iii) we get,
`z = -4`

And From (i) we get,
`y = 3*1 +(-4) +3 = 3 -4 +3 = 2`

Therefore, the value of x is 1; y is 2 and z is -4.