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

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:

$$\begin{gathered} \frac{x}{9-4}=\frac{y}{3+9m}=\frac{1}{4m+3} \\ \Rightarrow x=\frac{5}{4m+3},y=\frac{9m+3}{4m+3} \end{gathered}$$


$$\begin{gathered} \mathrm{For}x\mathrm{to}\mathrm{be}\mathrm{integer}\mathrm{we}\mathrm{have},4m+3=1,-1,5\mathrm{and}-5 \\ \Rightarrow m=\frac{-1}{2},-1,\frac{1}{2}\mathrm{and}-2 \end{gathered}$$
Hence, the integral values of m are $-$1 and $-$2.