Question

How many solutions can a single variable linear equation contain?

Select all that apply.

two solutions
one solution
no solution
infinite number of solutions

Answer 1

A single variable linear equation can contain:

- **one solution**: This occurs when the equation represents a line that intersects the x-axis at a single point.
- **no solution**: This occurs when the equation represents a contradiction (for example, \(x = 3\) and \(x = 5\) simultaneously).
- **infinite number of solutions**: This occurs when the equation simplifies to a tautology (for example, \(0 = 0\) after simplification).

However, a single variable linear equation cannot contain **two solutions** because a linear equation in one variable represents a straight line, which can intersect a point at most once.

So the correct selections are:
- one solution
- no solution
- infinite number of solutions