x 2y 3z 1 2x 5y 3z 1 x bz c Find all values of b and

x + 2y + 3z = 1

2x + 5y + 3z = -1

x + bz = c

Find all values of b and c (if they exist) such that all three planes are the same plane

Solution

all three planes are not the same plane

x + 2y + 3z = 1

2x + 5y + 3z = -1 are not linearly dependant

so all 3 planes are different

b and c doesnot exust