The number of integral values of `m` for which the x-coordinate of the point of intersection of the lines `3x+4y=9` and `y=m x+1` is also an integer is (a) 2 (b) 0 (c) 4 (d) 1

Options

A. 2
B. 0
C. 4
D. 1

Explanation

To find the number of integral values of \( m \) for which the x-coordinate of the point of intersection of the lines \( 3x + 4y = 9 \) and \( y = mx + 1 \) is also an integer, we can follow these steps:

### Step 1: Write the equations
We have the two equations:
1. \( 3x + 4y = 9 \) (Equation 1)
2. \( y = mx + 1 \) (Equation 2)

### Step 2: Substitute Equation 2 into Equation 1
...