Question

No Solutions
When you solve equations with NO solutions....do you get? (choose one below)
0x = 0
correct scenario
Ox = any #
x= any # (circle the
What does it mean on a graph to have no solutions? Explain what you would see.

Answer 1

When you solve equations with no solutions, you typically encounter a situation where the equations represent lines that are parallel to each other. The correct choice among the options you provided is:

- **0x = 0** (this represents an identity and has infinitely many solutions, so it's not correct)
- **Ox = any #** (this doesn't make sense as it implies no x-variable)
- **x = any #** (this implies there are infinite solutions as well)

For equations with **no solutions**, you would commonly have a scenario that resembles **two parallel lines**, for example:

1. **y = 2x + 3** (line 1)
2. **y = 2x - 1** (line 2)

In this case, both lines have the same slope (2), meaning they are parallel, but they have different y-intercepts (3 and -1). Because the lines never intersect, there are no points that satisfy both equations simultaneously—hence, there are no solutions.

### What it means on a graph to have no solutions:
- On a graph, having no solutions means that the lines (or curves) representing the equations do not intersect at any point. You'll visually see two distinct lines running parallel to each other without any crossing point.
- In summary, on a graph with no solutions, you would see parallel lines that are always the same distance apart, never meeting.