Solution of the linear pair of equations -4x – y = 6 and 3x + 5y = 16 by the graphical method then the point of intersection is __________ .

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(3,2)

(4,5)

(2,2)

(2,4)

answer is C.

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Detailed Solution

Let us assume the two equations as: -
⇒ 4x−y = 6…………..(1)
⇒ 3x+5y = 16………..(2)
Considering equation (1), we have,
⇒ 4x−y = 6, substituting x = 0, we get,
⇒ − y = 6
⇒ y = − 6
Substituting y = 0, we get,

⇒ 4 x = 6 ⇒ x = 64 ⇒ x = 32

Therefore, the two points are:

− A (0, − 6)

and

B 32, 0

.
Now, considering equation (2), we have,

⇒ 3 x + 5 y = 16

, substituting

x = 0

, we get,

⇒ 5 y = 16 ⇒ y = 165

Substituting

y = 0

, we get,

⇒ 3 x = 16 ⇒ x = 163

Therefore, the two points are: -

C 0, 165

and

D 163, 0

.
Therefore, the graph of the two functions can be plotted as: -

https://www.vedantu.com/question-sets/c1a33970-5ed3-470e-95c4-c0dd88a7205d2064013030167884775.png

Here, we are assuming the point of intersection of the two lines as P. On observing the graph we can see that the point of intersection of the two lines is given by the coordinates P (2, 2).

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