If a system of equations has an infinite number of solutions, what is it called? Choose the best answer. Enter the number associated with that answer for your response.
inconsistent and dependent system of equations
consistent system of equations
dependent system of equations
consistent and dependent system of equations
3. dependent system of equations
3. dependent system of equations
To determine the type of system of equations that has an infinite number of solutions, we need to understand the conditions for this to occur.
A consistent system of equations is one that has one unique solution, meaning that there is a specific set of values that satisfies all the equations simultaneously.
An inconsistent system of equations is one that has no solution, which means there is no set of values that satisfies all the equations simultaneously.
A dependent system of equations is one that has infinitely many solutions. This occurs when all the equations in the system are equivalent or can be derived from each other by performing valid algebraic operations. In other words, one equation can be obtained by adding, subtracting, or multiplying another equation(s) in the system.
Therefore, the correct answer is:
3. dependent system of equations.