The number of integer values of , for which the -coordinate of the point of intersection of the lines and is also an integer, is
- A.2
- B.0
- C.4
- D.1
Show answer and solution
Correct option: A
Solution
Substitute y = mx + 1 into 3x + 4y = 9:
3x + 4(mx + 1) = 9 → x(3 + 4m) = 5 → x = 5/(3 + 4m).
For x to be an integer, (3 + 4m) must be a divisor of 5, i.e., 3 + 4m ∈ {±1, ±5}.
- 3 + 4m = 1 → m = -1/2 (not integer)
- 3 + 4m = -1 → m = -1 (integer) ✓
- 3 + 4m = 5 → m = 1/2 (not integer)
- 3 + 4m = -5 → m = -2 (integer) ✓
So there are exactly 2 integer values of m.
3x + 4(mx + 1) = 9 → x(3 + 4m) = 5 → x = 5/(3 + 4m).
For x to be an integer, (3 + 4m) must be a divisor of 5, i.e., 3 + 4m ∈ {±1, ±5}.
- 3 + 4m = 1 → m = -1/2 (not integer)
- 3 + 4m = -1 → m = -1 (integer) ✓
- 3 + 4m = 5 → m = 1/2 (not integer)
- 3 + 4m = -5 → m = -2 (integer) ✓
So there are exactly 2 integer values of m.
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