Find all values of a and k for which the system has no solution.

Question

2y + z = 1

2x + 4y + az = 0

x + 3y - z = k

where a and k are constants.

Find all values of a and k for which the system has no solution.

Answer 1

a system of equations has no solution when they are inconsistent

for example x=1 and x=2 are an inconsistent system with no real solution

2y+z=1

2x+4y+az=0

x+3y-z=k

is more complicated.

3rd equation is same as 2x+6y -2x =2k

which is inconsistent with 2nd equation

when a=-2 and k=0

other values of a and k create inconsistencies