If the system of simultaneous linear equations 3 x-4 y+k z+13=0, x+2 y-z-9=0 and k x-y+3 z+7=0 has a unique solution x= , y= , z= for k m and 2 - =8 , then +m=

Step-by-step solution

aligned & | array ccc 3 & -4 & k 1 & 2 & -1 k & -1 & 3 array | 0 & 3(6-1)+4(3+k)+k(-1-2 k) 0 & 15+12+4 k-k-2 k^2 0 & 2 k^2-3 k-27 0 2 k^2-9 k+6 k-27 0 & k 9 2 ,-3 aligned On putting x= , y= , z= inequation gathered x+2 y-z-9=0 +2 - -9=0 +8-9=0 [It is given that 2 - =8 ] =1 gathered As k m m=9 / 2-3 +m=1+ 9 2 = 11 2 or +m=1-3=-2