Let us summarize the three cases possible with respect to a pair of linear equations.

Case-1: There is a unique solution

In this case, the two lines will intersect each other at a unique point. The coordinates of that point will be the solution to the pair of linear equations:

Solution to pair of linear equations

Case-2: There is no solution

In this case, the two lines will be parallel to each other, so that there is no common point (of intersection):

Parallel lines with no intersection

Case-3: There are infinitely many solutions

In this case, the two lines happen to coincide. This occurs because the two linear equations are essentially the same, if you remove an appropriate common factor from one of the two equations. In the following figure, we have drawn two lines which coincide, so there appears to be only one line:

Infinite solutions to pair of linear equations

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