Question

Write the condition for unique solution of linear equation:

Answer 1

Hint: The significance of a unique solution is that the two lines that we are talking about are intersecting or meeting each other at only a single point, therefore giving a unique or a single solution.

Complete step-by-step answer:

In order to be more clear, let's take into consideration an example.

Let us suppose that we have two lines having lines equations as:
$ax + by + c = 0$ and $px + qy + d = 0$

Then it will have a unique solution if and only if we have only one pair of (x, y) satisfying the equations after evaluation.

Taking mathematical expression into consideration then the general equation of line having equation as mentioned above in equation will have a unique solution if and only if
$\dfrac{a}{b} \ne \dfrac{p}{q}$

That is the ratio of coefficients of the first and the second term of the equations must not be equal to each other.

Note: The more physical interpretation that we can infer from the concept of two linear equations having a linear equation is that if the lines are neither parallel nor coincident then it will always have a unique solution. Parallel lines give rise to no solution whereas coincident lines refer to infinitely many solutions.