Question

if you solve a system of equations and both variables cancel out leaving a true statement like 0 = 0, what does it mean? a. the equations are not linear. b. the system has infinitely many solutions. c. the system has exactly one solution. d. the system has no solution.

Explanation:

Step1: Analyze system - of - equations concept

When in a system of linear equations, if after simplification we get a statement like \(0 = 0\), it means the two equations in the system are essentially the same or dependent.

Step2: Determine solution type

Dependent linear - equations have infinitely many solutions because every point that satisfies one equation also satisfies the other.

Answer:

b. The system has infinitely many solutions.