Question

Can you help me understand question number 2?

Answer 1

Given:

`\(x,y)`

To find:

The test point is in the solution set for the linear inequality.

Solution:

The inequality is

`5x-7y<0`

Here,
`x\in I, y\in I`. 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

`5(-2)-7(-1)<0`

`-10+7<0`

`-3<0`

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

`5(-4)-7(-3)<0`

`-20+21<0`

`1<0`

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

`5(-2)-7(-4)<0`

`-10+28<0`

`18<0`

This statement is false. So, the point (-2,-4) is not in the solution set.

Therefore, the correct option is A.