Question

Can a system of linear equations have exactly two solutions?
1) True
2) False

Answer 1

False, a system of linear equations cannot have exactly two solutions; it can only have one solution, no solution, or infinitely many solutions.

Step-by-step explanation:

The statement that a system of linear equations can have exactly two solutions is false. When we consider the possible outcomes for a system of linear equations, there are three potential scenarios:

• Exactly one solution (the lines intersect at one point).
• No solution (the lines are parallel and never intersect).
• Infinitely many solutions (the lines are coincident, meaning they lie on top of each other).

Therefore, a system of linear equations can't have exactly two solutions because this would imply that two straight lines intersect at two different points, which cannot happen in Euclidean geometry.