Answer:
The value of x=1; y=2; z=-4
Solution:
As given in the problem,
[tex]3x - y + z = -3[/tex]
[tex]=> y = 3x +z+3[/tex] -----(i)
[tex]-2x + y - 2z = 8[/tex]
[tex]=> y =2x +2z +8[/tex] ----- (ii)
So From (i) and (ii) we get,
[tex]3x +z+3 = 2x +2z +8[/tex]
[tex]=> 3x + z +3 -2x- 2z -8 =0[/tex]
[tex]=> x -z -5 =0[/tex]
[tex]=> z= x-5[/tex] -----------(iii)
Now, [tex]-4x + 3y - z = 6[/tex]
[tex]=> -4x + 3(3x+z+3) - z =6[/tex] (// substituting value of y from (i))
[tex]=> -4x +3(3x+x-5+3)-(x-5) = 6[/tex] (//substituting value of z from (iii))
[tex]=> -4x + 12x -6 -x +5 =6[/tex]
[tex]=> 7x -1 =6[/tex]
[tex]=> 7x = 7[/tex]
[tex]=> x = 1[/tex]
So from (iii) we get, [tex]z = -4[/tex]
And From (i) we get, [tex]y = 3\times1 +(-4) +3 = 3 -4 +3 = 2[/tex]
Therefore, the value of x is 1; y is 2 and z is -4.
