Question

For each system of linearesuations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose thebest description of its solution. If the system has exactly one solution, give its solution.System ASystem BSystem C

Answer 1

A system of equations is independent when it has exactly 1 solution.

A system of consistent equations is independent when it has an infinte number of solutionshen it has an i

Looking at system A, the lines of the two equations are parallel. This means that they will never intersect and this implies that there is no solution. They are inconsistent

Looking at system B, the lines of the two equations are coincide. This means that they are the same lines. Since there is no point of intersection, there is an infinite number of solutions hence, they are dependent. on. They e inconsis and dependent

Looking at system C, the lines of the two equations are coincide. This means that there is only one solution and it's at the point of intersection solution. They are consistent and independent. Looking at the point of intersection, the solution would be the x and y coordinates of this point. Hence, solution = (1, 2)

Tis implies that there is no solution