The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:
The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:
Option 1 -
1
Option 2 -
3
Option 3 -
0
Option 4 -
2
Asked by Shiksha User
-
1 Answer
-
Correct Option - 1
Detailed Solution:Given equations:
3x + 4y = 9
y = mx + 1 (assuming this from the substitution)Substitute y into the first equation:
3x + 4 (mx + 1) = 9
3x + 4mx + 4 = 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., ±1, ±5.
- 3 + 4m = 1 => 4m = -2 => m = -1/2
- 3 + 4m = -1 => 4m = -4 => m = -1 (Integer value)
- 3 + 4m = 5 => 4m = 2 => m = 1/2
- 3 + 4m = -5 => 4m = -8 => m = -2 (Integer value)
The two integral values for m are -1 and -2.
Taking an Exam? Selecting a College?
Get authentic answers from experts, students and alumni that you won't find anywhere else
Sign Up on ShikshaOn Shiksha, get access to
- 65k Colleges
- 1.2k Exams
- 688k Reviews
- 1800k Answers