Understanding Consistency in Systems of Linear Equations: Explained by a Math Specialist

If a system of linear equations has infinitely many solutions, then it may be inconsistent.

Actually, if a system of linear equations has infinitely many solutions, then it is considered consistent

Actually, if a system of linear equations has infinitely many solutions, then it is considered consistent. Inconsistent systems have no solution or a contradiction. Let me explain further.

A system of linear equations consists of two or more equations with the same variables. The goal is to find the values of the variables that satisfy all the equations simultaneously. There are three possible outcomes for a system of linear equations:

1. Consistent system: This occurs when the system has at least one solution, and it can have both a unique solution or infinitely many solutions. When a system has infinitely many solutions, it means that the equations are not independent and can be simplified to form a single equation. In this case, any value that satisfies the simplified equation will be a solution to the original system.

2. Inconsistent system: This occurs when the system has no solution or a contradiction. In other words, the equations in the system are inconsistent with each other, making it impossible to find a set of values that satisfies all the equations.

3. Dependent system: This is a special case of a consistent system where there are infinitely many solutions. The equations in a dependent system are not independent, and they can be simplified to form a single equation (or a set of equations) with infinite solutions. In this case, any value that satisfies the simplified equation(s) will be a solution to the original system.

So, to conclude, if a system of linear equations has infinitely many solutions, it is definitely consistent, not inconsistent.

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