If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system? a) there are infinitely many solutions b) the lines in a system cannot be parallel c) there is no solution d) there is exactly one solution

 The correct options are

(A)  there are infinitely many solutions.

(C)  there is no solution.

Step-by-step explanation:  Given that the graphs of the linear equations in a system are parallel.

We are to select the meaning about the possible solutions of the system.

The solution of a system of linear equations is given by the points of intersection of the line graphs of two equations.

Since the two equations are linear, so their graphs will be straight lines.

So, there are two possible cases for the solution of such systems.

(i) If the two line graphs coincide with each other, then obviously they are parallel. Here, the lines intersect at each other at every point that lies on the two lines. So, each point on the lines will be a solution to the system.

Therefore, in this case, there will be infinitely many solutions.

(ii) If the two line graphs are parallel but do not coincide, then there will be no point of intersection. So, there will no solution to the system.

Therefore, in this case, there will be no solution.

Thus, the correct options are

(A)  there are infinitely many solutions.

(C)  there is no solution.

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step-by-step explanation:

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