Question

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.

Answer 1

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:

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

⇒ m = \(-\frac{1}{2}\) ,-1,\(\frac{1}{2}\) and -2 

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