Determine a relationship between the constantsa and b if the system below is to have infinitely many solutions.

x+ 2y + z = 1 + b

−x − 2y + z = a + 2b − 1

2x + 4y + 3z = 2b + 2

Okay so this is what I have so far:

[ 1 2 1 | 1+b ]

[-1 -2 1 | a+2b-1]

[ 2 4 3 | 2b +2 ]

.

.

.

.

After ysing the G-J method, I get all the way to

[1 0 3/2 | 1/2a + b]

[0 0 2 | a + 3b ]

[0 0 0 | -2 ]

SO its in row-reduced form now...I think. Feeling a bit stuck at this point.