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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)

User Derick
by
7.1k points

1 Answer

6 votes

Answer:

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.

User Jkhosla
by
6.8k points