Question

what is consistent and inconsistent define in right way with example​

Answer 1

Answer:

Consistent System

To sketch the graph of pair of linear equations in two variables, we draw two lines representing the equations. The following cases are possible:

i) If both the lines intersect at a point, then there exists a unique solution to the pair of linear equations. In such a case, the pair of linear equations is said to be consistent.

Linear Equation- Having one solution

In the graph given above, lines intersect at point P(x,y) which represents the unique solution of the system of linear equations in two variables.

Algebraically, if a1/a2 ≠ b1/b2 then, the linear equations’ pair is consistent.

ii) Consider two lines having equation to be-

a1x+b1y+c1 = 0 and

a2x+b2y+c2 = 0

Let these lines coincide with each other, then there exist infinitely many solutions since a line consists of infinite points. In such a case, the pair of linear equations is said to be dependent and consistent. As represented in the graph below, the pair of lines coincides and therefore, dependent and consistent.

Linear Equation- Having Infinite Solution

Algebraically, when a1/a2 = b1/b2 = c1/c2 , then the lines coincides and the pair of equations is dependent and consistent.

Inconsistent System

i) Consider the equation of the lines to be-

a1x+b1y+c1 = 0 and

a2x+b2y+c2 = 0

Let both the lines to be parallel to each other, then there exists no solution, because the lines never intersect.

Linear Equation- Having no solution ( Parallel Lines)

Algebraically, for such a case, a1/a2 = b1/b2 ≠ c1/c2 and the pair of linear equations in two variables is said to be inconsistent.

As shown in the graph above, the pair of lines a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are parallel to each other. Therefore, there exists no solution for such a pair.