Question

If solving a system of linear equations by elimination or substitution I get that 0=0, as final or intermediate step depending on the system, it means (check all that apply)

I have definitely made a mistake and need to review the result

If the system of equations is 2 linear equations in 2 variables, there is infinity number
of solution

If the system of equations is 3 linear equations in 3 variables, there might be infinite
number of solutions

If the system of equations is n linear equations in n variables, there is one unique solution

Answer 1

If I get 0=0 then it means:

• If the system of equations is 2 linear equations in 2 variables, there is infinity number of solutions
• If the system of equations is 3 linear equations in 3 variables, there might be infinite number of solutions

Explanation:

Linear equation systems can consist of two or three equations with two or three unknowns respectively.

A system of linear equations in two variables has infinite solutions when the lines made by them overlap each other and similarly a system with three variables has infinite solutions when two lines overlap each other and third plane is parallel to them

Hence,

If I get 0=0 then it means:

• If the system of equations is 2 linear equations in 2 variables, there is infinity number of solutions
• If the system of equations is 3 linear equations in 3 variables, there might be infinite number of solutions