How to dissolve shared line segments together in QGIS?

Question

I have 2 features which are lines on a single layer re-projected to ESPG:2039.

I wish to combine them into one MultiLineString but in a way that their common part is merged to a single LineString. I'm using QGIS 3.6.2

I snapped their geometries to the grid and tried to dissolve them together. But when I add start vertices (green) and end vertices (red) to be displayed, I can see that I have 2 lines in the MultiLineString instead of 5 lines:

When I run the "intersect" tool on the lines as seperate layers, I get that they do intersect in the joint area (blue line):

How can I make the joint part be dissolved together to a single line? Data can be found here as SHP file: http://www.filedropper.com/2lines

UPDATE: I tried to use the "Remove duplicates" as suggested by Erik, but it didn't do a thing.

Answer 1

In order to merge multiple features into one used the Merge Selected Features function. Choose all the item you want to merge, they don't need to touch each other.

Make sure that the Advanced Digitizing Toolbar is on, and click on the Merge Selected Features function.

Know you need to choose how to merge your features. In a table with few rows it's easy, in a larger one you need to make sure that you will not lose data you need.

Now, all the rows in the table have been merged into one.