I'm pretty stuck trying to solve the below circuit. I need to find the node voltages and branch currents. I've tried it using mesh, nodal and superposition analyses, but I just can't get the right answer. I'm really not sure where I'm going wrong.
Using the mesh analysis, I took the clockwise left-hand loop as x and the clockwise right-hand loop as y.
Then: $$10V=10I_x+30(I_x-I_y)$$ $$10V=40I_x-30I_y$$ And: $$6V=40I_y+30(I_y-I_x)+20I_y$$ $$6V=90I_y-30I_x$$ Solving these gives $$I_x=0.4A, I_y=0.2A$$ But I've been told that $$I_x=0.267A, I_y=-0.022A$$ I know my solution is wrong anyway, because I end up with a resistor supplying power to the circuit. Where am I going wrong?