Write the integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer.

Given:

Lines y = mx + 1 and 3x + 4y = 9

To find:

The integral values of m

Explanation:

The given lines can be written as

mx – y + 1 = 0 … (1)

3x + 4y – 9 = 0 … (2)

Solving (1) and (2) by cross multiplication, we get:

⇒ x

y
For x to be integer we have, 4m + 3 = 1, -1, 5 and -5

⇒ m,-1,and -2
Hence, the integral values of m are -1 and -2.