Question

Which statement describes the system of equations? The system has infinitely many solutions. The system has no solution. The system has one solution The system has one solution

Answer 1

A system of equations has infinitely many solutions when there are more unknowns than equations.

Step-by-step explanation:

The statement 'The system has infinitely many solutions' describes a system of equations where the number of unknowns is larger than the number of equations. In this case, there are more variables to solve for than equations available, resulting in an infinite number of possible solutions.

For example, consider the system of equations:

x + y = 3

2x + 2y = 6

These equations are equivalent, meaning they represent the same line on a coordinate plane. Therefore, every point on the line is a solution to the system, resulting in infinitely many solutions.