If the system of equations (k+1)^3 x+(k+2)^3 y =(k+3)^3(k+1) x+(k+2) y =k+3x+y =1 is consistent, then the value of k is

Step-by-step solution

System of equations (k+1)^3 x+(k+2)^3 y=(k+3)^3(k+1) x+(k+2) y=(k+3)x+y=1 is consistent. Since, the given system of equations are consistent. Then D=0 and Also, (D₁=D₂=D₃=0 ) have infinitely many solutions. By Crammer Rule D= | array ccc (k+1)^3 & (k+2)^3 & (k+3)^3 (k+1) & (k+2) & (k+3) 1 & 1 & 1 array |=0 C₂ C₂-C₁C₃ C₃-C₁D= | array ccc (k+1)^3 & (k+2)^3-(k+1)^3 & (k+3)^3-(k+1)^3 (k+1) & (k+2)-(k+1) & (k+3)-(k+1) 1 & 0 & 0 array |=0D= | array ccc (k+1)^3 & (3 k^2+9 k+7 ) & (6 k^2+24 k+26 ) (k+1) & 1 & 2 1 & 0 & 0 a