Creating a dynamic filter in Matrix table

As i understand you need to have a slicer and when user selects System 1 in that slicer, show only Report IDs that are associated with System 1, but keep all System columns visible in the matrix.

I suggest:

1. Create a Disconnected Slicer Table (via DAX)

Since you mentioned you cannot create physical tables easily, create this as a calculated table in the semantic model:

System Slicer = DISTINCT ( 'Table 2'[System Name] )

• This table should NOT have any relationship to your other tables.

2. Create the Row Filter Measure

Report Has Selected System = 
VAR SelectedSystems = VALUES ( 'System Slicer'[System Name] )
RETURN
    CALCULATE (
        COUNTROWS ( 'Table 2' ),
        'Table 2'[System Name] IN SelectedSystems,
        ALLEXCEPT ( 'Table 1', 'Table 1'[Report ID] )
    ) + 0

3. Apply to the Matrix Visual

1. Select your Matrix visual.
2. In the Filters pane → Filters on this visual.
3. Drag the measure Report Has Selected System into the filters.
4. Set the filter to is 1.

Now when the user selects one or more systems in the slicer, the matrix will:

• Filter the rows (Report IDs) to only those associated with the selected system(s)
• Keep all columns (System 1, System 2, System 3, etc.) visible

Slicer Setup

• Use the System Slicer table in a Dropdown or List slicer.
• Allow multi-select if needed.

Alternative (If you cannot create the calculated table)

You can use the original 'Table 2'[System Name] in the slicer, but then you must use Edit interactions to stop the slicer from filtering the matrix directly, and rely only on the measure above. However, the disconnected table approach is much cleaner.