Given:
[tex]\{(x,y)|5x-7y<0, x\in I, y\in I\}[/tex]
To find:
The test point is in the solution set for the linear inequality.
Solution:
The inequality is
[tex]5x-7y<0[/tex]
Here, [tex]x\in I, y\in I[/tex]. It means, both x and y both are integers. So, the option D is incorrect because 1.5 and 3.5 are not integers.
For option A, the point is (-2,-1).
Putting x=-2 and y=-1 in the given inequality, we get
[tex]5(-2)-7(-1)<0[/tex]
[tex]-10+7<0[/tex]
[tex]-3<0[/tex]
This statement is true. So, the point (-2,-1) is in the solution set.
For option B, the point is (-4,-3).
Putting x=-4 and y=-3 in the given inequality, we get
[tex]5(-4)-7(-3)<0[/tex]
[tex]-20+21<0[/tex]
[tex]1<0[/tex]
This statement is false. So, the point (-4,-3) is not in the solution set.
For option C, the point is (-2,-4).
Putting x=-2 and y=-4 in the given inequality, we get
[tex]5(-2)-7(-4)<0[/tex]
[tex]-10+28<0[/tex]
[tex]18<0[/tex]
This statement is false. So, the point (-2,-4) is not in the solution set.
Therefore, the correct option is A.