The system tray does only give more information (on the clock etc) because it has the space to do so. Please understand that the system tray is part of the taskbar and as such will resize to whatever size the taskbar is.
What you need to do is ensure that the taskbar is unlocked (right-click and make sure there is no checkbox in front of "lock the taskbar". If so, click it, to remove the checkbox.
Now, hover the mouse to the edge of the taskbar that is not touching the edge of the screen (the taskbar touches the edge of the screen on 3 sides, and the desktop on 1 side, you want to find this last edge.)
The mouse cursor will change to a resize icon. Now drag and hold the left mouse button and move the mouse as far to the edge of the screen as possible, making it smaller. It will move in intervals because the taskbar has fixed widths. Just move it as far as you can until the taskbar has the desired size.
For the best results, drag the taskbar in its center.
You may need to reorder certain taskbar elements. You can do this by dragging the | beam at the very left of each taskbar section (if applicable)
Once done, lock the task bar again by right-clicking the bar and select Lock the taskbar.
I don't understand your focus on the ‘‘system tray’’. Is the entire task bar double height? If so, do you want to change the entire task bar (back?) to being single height? A screen shot might help. – G-Man Says 'Reinstate Monica' – 2017-11-03T08:38:15.397
Have you tried: Right-click the taskbar and uncheck "Lock the taskbar". This will allow you to move your taskbar to increase or decrease in size. At the edge of the taskbar, a line symbol will show (with arrows). Drag the taskbar with the cursor, the mouse, in the direction of decreasing or increasing. Then if you want to, relock the taskbar. – El8dN8 – 2017-11-03T08:44:20.723
Hi G-Man,I am a beginner- I should have simply said only "taskbar".Please forget the vsystem tray. – monikazuck – 2017-11-03T08:46:28.383
E18,I tried your suggestion but in Windows 7, there was no little symbol and I could not drag the six little icons into a single line even after I got rid of the clock,(time,day and date)Any ideas?Thank you very much.Also the left taskbar with larger icons is still on two lines/rows instead on one like before. – monikazuck – 2017-11-03T09:41:03.760