Question
You can tell by looking at the graphs of the two lines how many solutions there will be to the system of equations. Match the description of the 2 lines when you graph them with the number of solutions that system would have.
(3 points)
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.
You will see the 2 lines are parallel lines
You will see the two lines intersect at only one point
You will see the 2 lines graphed on top of each other and form the same exact line
(3 points)
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.
You will see the 2 lines are parallel lines
You will see the two lines intersect at only one point
You will see the 2 lines graphed on top of each other and form the same exact line
Answers
GPT-4o mini
To match the descriptions of the two lines with the number of solutions to the system of equations, the connections are as follows:
1. **You will see the two lines are parallel lines** - This means there will be **no solutions** since parallel lines never intersect.
2. **You will see the two lines intersect at only one point** - This means there will be **one solution** since the intersection point represents the solution to the system.
3. **You will see the two lines graphed on top of each other and form the same exact line** - This means there will be **infinitely many solutions** since every point on the line is a solution to the system.
So to summarize:
- **Parallel lines** → **No solutions**
- **Single intersection point** → **One solution**
- **Same exact line** → **Infinitely many solutions**
1. **You will see the two lines are parallel lines** - This means there will be **no solutions** since parallel lines never intersect.
2. **You will see the two lines intersect at only one point** - This means there will be **one solution** since the intersection point represents the solution to the system.
3. **You will see the two lines graphed on top of each other and form the same exact line** - This means there will be **infinitely many solutions** since every point on the line is a solution to the system.
So to summarize:
- **Parallel lines** → **No solutions**
- **Single intersection point** → **One solution**
- **Same exact line** → **Infinitely many solutions**