Question

If a pair of linear equations is consistent and dependent. In the below graph the lines are ________________ .
A) Parallel
B) Coincidence
C) Intersecting
D) Divergence

Answer 1

Hint: If a system has at least one solution, it is said to be consistent. If a consistent system has an infinite number of solutions, it is dependent. In the given question it is written that the linear equation is consistent and dependent at the same time.

Complete step by step answer:
It is given that the Lines formed by the linear equation will have at least one value and it may have infinite solutions as well but zero solution is not an option If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution. So clearly option A is incorrect. As We know that it has only one solution so it is not independent, It is a dependent system of equations So the graph will also not intersect to each other. Hence option C is also incorrect.
If a consistent system has an infinite number of solutions, it is dependent . When you see the graph of equations, both equations represent the same line. So it is clear that in the solution only one line is shown. So Clearly option (B) is correct. The lines are coincidental to each other.

Note: From the graph only it could have been concluded that it's not parallel or intersecting as only one line was given but for divergence also there must exist a point of discontinuity which clear is not visible so it is also not divergence which leaves us with only one option that is the graph is coincidental.