Determine whether of symstems of equations have one solution, two solutions, infinite solutions or no solutions.(1 point)

Question

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
COLUMN 1
One Solution
Two Solutions
Infinite Solutions
No Solutions

Skip to navigation

Answer 1

To determine the type of solution for a system of equations, we can analyze how the lines represented by these equations relate to each other. Here are the definitions for each category:

• One Solution: The lines intersect at exactly one point.
• Two Solutions: Typically applies to nonlinear systems (like a circle intersecting a line in two points).
• Infinite Solutions: The lines are identical (they overlap completely).
• No Solutions: The lines are parallel and never intersect.

If you provide specific systems of equations, I can help you identify which category they fall into. Otherwise, here's how you would typically categorize them based on the general equations:

1. One Solution: If two lines have different slopes.
2. Two Solutions: Commonly seen in the context of curves and lines (e.g., a circle and a line).
3. Infinite Solutions: If two equations are equivalent (e.g., \(2x + 3y = 6\) and \(4x + 6y = 12\)).
4. No Solutions: If two lines have the same slope but different intercepts (e.g., \(y = 2x + 3\) and \(y = 2x - 1\)).

Let me know if you need specific equations analyzed!