If the system of equations k x + y + 2 z = 1 3 x - y - 2 z = 2 - 2 x - 2 y - 4 z = 3 has infinitely many solutions, then k is equal to ______ .

Step-by-step solution

If the system of equations P 1 :   k x + y + 2 z = 1 P 2 :   3 x - y - 2 z = 2 P 3 :   - 2 x - 2 y - 4 z = 3 Which are equivalent to equations of planes. We observe 5 P 2 - P 1 = 3 P 3 So, 15 - K = - 6 ⇒   K = 21