Question

If solving a system of linear equations by elimination or substitution I get that 2=3, it means (check all that apply)

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 is infinity number of solutions
If the system of equations is 2 linear equations in 2 variables, the system has no solutions
If the system of equations is 3 linear equations in 3 variables, the system has no solutions

Answer 1

If solving a system of linear equations by elimination or substitution leads to the statement 2=3, it means that the system has no solution.

Step-by-step explanation:

When solving a system of linear equations by elimination or substitution, if you end up with the statement 2=3, it means that the system has no solution. This applies to both 2 linear equations in 2 variables and 3 linear equations in 3 variables. In both cases, the system is inconsistent and cannot be solved. This is because the statement 2=3 is a contradiction and there is no way to find values for the variables that satisfy all the equations simultaneously.

Answer 2

If I get 2=3 in solving the system, it means the following:

• If the system of equations is 2 linear equations in 2 variables, the system has no solutions
• If the system of equations is 3 linear equations in 3 variables, the system has no solutions

Step-by-step explanation:

The solution of linear system of equations implies that a point has to be found that holds true on all equations involved.

The system may consist of two equations involving two unknowns or may consist of three equation with three unknowns.

When a system of equation has no solution, the variables are removed in solving the equations and we get an equation or values in the form.

constant = constant

So,

If I get 2=3 in solving the system, it means the following:

• If the system of equations is 2 linear equations in 2 variables, the system has no solutions
• If the system of equations is 3 linear equations in 3 variables, the system has no solutions