Categorize the following qualities of systems of equations.

Question

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!