Solve for a, b, c and d (the answers are not all 0)

a - 3b = 0
-a + 2b +2c - d = 0
b + c +d = 0

I can't seem to solve for all them, please show steps. Thanks.

You have 3 equation with 4 unknowns, so you can't possibly solve for all of them. You'd need an additional independent equation.

What you can do is solve for 3 of the variables in terms of the 4th variable:

Adding all equations together, we get:
.a - 3b . . . . . . . = 0
-a + 2b + 2c - d = 0
. . . . . b + c + d = 0
--------------------------
0a + 0b + 3c + 0d = 0
c = 0

So now we have:
a - 3b = 0
-a + 2b - d = 0
b + d = 0 ---------> d = -b

Substituting d with -b in second equation, we get:
-a + 2b + b = 0
-a + 3b = 0

But this is just equivalent to first equation:
a - 3b = 0

So final solution is:
a = 3b
d = -b
c = 0

Here are possible solutions (there are infinitely many):
.. a .... b .... c .... d
.. 3 .... 1 .... 0 ... −1
. 12 ... 4 .... 0 ... −4
. −9 . −3 .... 0 ..... 3

I don't think you can because for 4 variables you need 4 equations.