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 solve the problem, we need 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 an integer.

### Step-by-Step Solution:

1. **Write the equations of the lines**:
- The first line is given by \( 3x + 4y = 9 \).
- The second line is given by \( y = mx + 1 \).

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