Question

the system of equations is solved using the linear combination method.
what does 0 = - 12 mean regarding the solution to the system?
there are no solutions to the system because the equations represent parallel lines.
there are no solutions to the system because the equations represent the same line.
there are infinitely many solutions to the system because the equations represent parallel lines.
there are infinitely many solutions to the system because the equations represent the same line.

Explanation:

In a system of linear - equations, when after using a method like linear combination, we get a false statement such as \(0=-12\), it means the system is inconsistent. Inconsistent systems of linear equations represent parallel lines, and parallel lines do not intersect. Since the solution of a system of linear equations is the point of intersection of the lines represented by the equations, there are no solutions when the lines are parallel.

Answer:

There are no solutions to the system because the equations represent parallel lines.