The solution to a system of two linear equations is x = 3 weeks; y = 9 feet

Question

Match the description with the correct statement.

options:

How could you get exactly two or three solutions to this linear system?

Answer 1

In the context of a system of two linear equations, you cannot obtain exactly two or three solutions. A system of linear equations can have:

1. No solution (the lines are parallel and never intersect)
2. Exactly one solution (the lines intersect at a single point)
3. Infinite solutions (the lines are coincident, meaning they are the same line)

Therefore, it is not possible to achieve exactly two or three solutions for such a system.

If you need a workaround, you might consider a scenario where you slightly modify the system (e.g., by adding constraints or equations) that allows for multiple points of intersection under certain conditions. However, in standard linear systems, only the outcomes mentioned above are applicable.