Question

The point of intersection of the lines x + y = 8 and x − y = 0 lies on the line mx − 2y = 0; the value of m is ______.

Options

• 3

• 4

• 2

• −2

Answer 1

The point of intersection of the lines x + y = 8 and x − y = 0 lies on the line mx − 2y = 0; the value of m is 2.

Explanation:

Given,

1st Equation:

⇒ x + y = 8

⇒ x = 8 − y ......(1)

2nd equation:

⇒ x − y = 0

⇒ x = y .........(2)

Substituting value of x from equation (2) in (1), we get:

⇒ y = 8 − y

⇒ y + y = 8

⇒ 2y = 8

⇒ y = `8/2​` = 4

From equation (2), we get:

⇒ x = y = 4

Point of intersection of lines x + y = 8 and x − y = 0 is (4, 4).

Given, point of intersection lies on the line mx − 2y = 0.

Substituting values we get:

⇒ 4m − 2 × 4 = 0

⇒ 4m − 8 = 0

⇒ 4m = 8

⇒ m = `8/4`​ = 2