Question

Which of the following is a solution of the system

x – 2y < 4 and y > – 2x – 5?
1. (1, -4)
2. (-8, 2)
3. (0,0)
4. (-3,0)

Answer 1

Option 3.

Explanation:

The given inequalities are

`x-2y<4`

`y>-2x-5`

If (a,b) is solution of given system of inequalities, then the above inequalities must be satisfy by the point (a,b).

For point (1,-4),

`(1)-2(-4)<4\Rightarrow 9<4` False

`-4>-2(1)-5\Rightarrow -4>-7` True

Since, first inequality is false for (1,-4) point, therefore (1,-4) is not the solution.

For point (-8,2),

`(-8)-2(2)<4\Rightarrow -12<4` True

`2>-2(-8)-5\Rightarrow 2>11` False

Since, second inequality is false for (-8,2) point, therefore (-8,2) is not the solution.

For point (0,0),

`(0)-2(0)<4\Rightarrow 0<4` True

`0>-2(0)-5\Rightarrow 0>-5` True

Since, both of inequalities are true, therefore (0,0) is a the solution.

For point (-3,0),

`(-3)-2(0)<4\Rightarrow -3<4` True

`0>-2(-3)-5\Rightarrow 0>-11` False

Since, second inequality is false for (-3,0) point, therefore (-3,0) is not the solution.

Hence, option 3 is correct.