Question

Categorize the following qualities of systems of equations.
1*
2*
3*

:: Consistent

:: Dependent



:: Inconsistent

:: Independent
One Solution
Answer by dragging items here
No Solutions
Answer by dragging items here
4*
5*
：：
6*
：：
•Both linear equations will have different slopes and possibly different y-intercepts.
Both linear equations will have the same slope
and y-intercepts.
Both linear equations will have the same slope, but different y-intercepts.
Infinitely Many Solutions
Answer by dragging items here

Answer 1

To categorize the qualities of systems of equations based on your provided items, we can use the following classifications:

1. **Consistent**:
- One Solution (Independent)
- Infinitely Many Solutions (Dependent)

2. **Inconsistent**:
- No Solutions

Now, let's assign the descriptions of the systems to their respective categories:

- **One Solution**:
- **Independent**: Both linear equations will have different slopes and possibly different y-intercepts.

- **No Solutions**:
- **Inconsistent**: Both linear equations will have the same slope but different y-intercepts.

- **Infinitely Many Solutions**:
- **Dependent**: Both linear equations will have the same slope and the same y-intercepts.

So, the complete categorization would look like this:

### Consistent
- **One Solution**: Independent (Different slopes)
- **Infinitely Many Solutions**: Dependent (Same slope and intercepts)

### Inconsistent
- **No Solutions**: Both linear equations will have the same slope but different y-intercepts.

Please let me know if you need further assistance or clarification!