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For each system of linear equations shown below, dassify 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

For Each System Of Linear Equations Shown Below Dassify The System As Consistent Dependent Consistent Independent Or Inconsistent Then Choose Thebest Descriptio class=

Sagot :

To answer this problem, first we need to understand the classifications available.

A system of two linear equations can have one solution, an infinite number of solutions, or no solution.

If a system has at least one solution, it is said to be consistent.

If a consistent system has exactly one solution, it is independent, if it has an infinite number of solutions, it is dependent.

If a system has no solution, it is said to be inconsistent.

Now, let's understand the graphs. On a linear system, the solution for the system is given by the interception of the graphs. If the lines intercept each other at one point, the system has one solution, therefore, it is consistent independent, If the lines are equal and intercept each other on every point, the system is consistent dependent, and finally, if the lines are parallel the system has no solution and it is inconsistent.

If we take a look on our group of systems, we have

System A: Incosistent

System B: Consistent Independent

System C: Consistent Dependent

The only system with only one solution is system B. The solution is given by its intercept, and as we can see on the graph, that happens at (0, 2).

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