If the system of equations 3 x+y+4 z=3 2 x+ y-z=-3 x+2 y+z=4 has no solution, then the value of is equal to :

Step-by-step solution

For no solution = 0 vmatrix 3 & 1 & 4 2 & & -1 1 & 2 & 1 vmatrix = 0 3( + 2) + 1(-1 - 2) + 4(4 - ) = 0 19 - = 0 = 19 & for = 19 _x = vmatrix 3 & 1 & 4 -3 & 19 & -1 4 & 2 & 1 vmatrix = 3(21) + 1(-1) + 4(-82) 0 no solution for = 19