Indicate whether each system is independent, inconsistent or dependent 4 ( 1-x) + y = 3 3 (1-y) - 4x = -=4y 1/3x - 1/6y = 1/3 1/6x + 1/4y= 0

solve each system by the addition method. indicate whether each system is independent, inconsistent or dependent

4 ( 1-x) + y = 3 .........................(1)
3 (1-y) - 4x = -4y .......................(2)

Solution We simplify (1) and (2), we get
-4x+y=-1 ..............(3)
-4x+y=-3 ..............(4)
By (3) (4), we get
-1=-3
a contradiction.

So, it is inconsistent.

1/3x - 1/6y = 1/3 ..................(1)
1/6x + 1/4y= 0 ..................(2)

Solution. (1)*6+(2)*4, we get
(2+2/3)x=2
i.e.,
x=3/4
By (2), we get
1/4y=1/6x=1/6*(3/4)=1/8

So, y=1/2

So, there is only one solution.

Hence, the system is independent