Solve for x,y, and z:3x - y + z = -3-2x + y - 2z = 8-4XL + 3y - z = 6

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.