Question

Identify the wrong statement with respect to a pair of linear equations
a) If lines are parallel there is no solution
b) If the lines are perpendicular to each other, there is no solution
c) many solutions if the lines coincide each other
d) a unique solution if they intersect ​

Answer 1

option B provided is incorrect

Given

• four statements regarding pair of linear equations

To find

• the incorrect statements among them

Solution

we are provided with four statements regarding system of linear equation and are asked to find the incorrect statement provided among them.

For a pair of linear equations that two lines could be either parallel, intersect at a point or coincide each other.

when two lines are parallel, there is no point of intersection between the or there is no common solution between them therefore, the option A provided is correct.

If two lines are perpendicular to each other at some point or other the lines must intersect each other in a two dimensional space therefore the option B provided is incorrect

For a pair of linear equations, it should have infinite number of solutions if the two lines coincide each other and it will have only a common point if it intersect at a point only. the option C and D are correct.

Answer 2

1. When two lines are parallel, there exists no solution and they are Inconsistent pair of linear equations .
2. When two lines intersect, they have an infinite solution and the pair of linear equations is consistent.
3. When two lines cross or intersect each other at a certain point, they have a unique solution at that point and the pair of linear equations is consistent.
4. Thus, from above we can conclude that option B is false.

Hence, option B is correct.

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