question_answer

Assertion (A): (Graphically, the pair of Linear equations \[\text{2x}-\text{y}-\text{5}=0\]and \[\text{x}-\text{y}-\text{3}=0\]represent intersecting lines.

Reason (R): The linear equations \[\text{2x}-\text{y}-\text{5}=0\] and \[\text{x}-\text{y}-\text{3}=0\]meet the y-axis at \[(0,3)\] and \[(0,-5)\].

A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

C) Assertion (A) is true but reason (R) is false.

D) Assertion (A) is false but reason (R) is true.

Correct Answer: C

Solution :

[c] The given system of linear equations is

\[2x-y-5=0\]      ...(1)

\[x-y-3=0\]        ...(2)

The two solutions of (1) and (2) are given below.

(1) x 3 2 y 1 -1

(2)        x 3 4 y 0 1

The graphical representation of the given pair of linear equations is as follows;

In the graph, we observe that the two lines intersect at the point \[B(2,-1)\].

So, \[x=2,\,\,y=-1\] is the required solution of the given pair of linear equations.

Also, we observe from the graph that the lines (1) and (2) meet the V-axis in the points \[E(0,-3)\]and \[F(0,-5)\]respectively.

So, Assertion: True; Reason: False.