Engineering Nodal analysis for OP amp circuit using superposition

[AbbeAbyss]

Homework Statement

http://www.wifstrand.se/Albert/stuff/p6.5-9.png

I'm stuck with finding v_o1 (voltage over the 10kohm resistor when all sources but the 3 V source, which I've labeled v_1, is set to zero); seems like it should be really simple but I'm missing an equation.

Homework Equations

http://www.wifstrand.se/Albert/stuff/p6.5-9-superpos.png

Nodal analysis for this figure gives

(v_a - 3)/8000 + (v_a - v_o1)/24000 = 0

The Attempt at a Solution

I have two unknown variables but I can't figure out what the second equation would be. The answer given in the initial problem statement suggests that v_a = 2 V and v_o1 = -1 (since a_1 = v_01 * v_1 = (-1) * 3 = -3) which satisfies the equation above but naturally I'd like to know what I'd need to solve it.

I can see that v_a - v_01 - 3 = 2 - (-1) - 3 = 0 but I'm not sure how to find that expression systematically and if it corresponds to KVL somehow.

 

[szynkasz]

We have ideal amplifier so both input nodes have the same potential, hence
V_a=0

 

[AbbeAbyss]

We have ideal amplifier so both input nodes have the same potential, hence
V_a=0

I messed up the calculation of the gain: it's a_1 = v_01 / v_1, not a_1 = v_01 * v_1 ...

So with your clarification on this (I believe I tried setting v_a to 0 initially but then I tried other stuff haphazardly since it didn't work with my faulty expression for a_1, LOL...), solving for v_01 in

(v_a - 3)/8000 + (v_a - v_o1)/24000 = 0

gives v_01 = -9 V and now it all makes sense.

Thanks.