Question

Which of the options is a solution for the following system of inequalities?

4x+y>3
x-y>2

(-2,-2)
(1,-5)
(0,0)
(5,-2)

Answer 1

for it to be a solution, it has to satisfy both inequalities.

using (5,-2)...x = 5 and y = -2

4x + y > 3
4(5) - 2 > 3
20 - 2 > 3
18 > 3.....correct

x - y > 2
5 - 2 > 2
3 > 2....correct

solution is (5,-2)

Answer 2

Option D.

Explanation:

The given system of inequalities are

`4x+y>3`

`x-y>2`

We need to find a solution for the following system of inequalities.

Check each point by these inequalities.

For (-2,-2)

`4(-2)+(-2)>3\Rightarrow -10>3` False

So, (-2,-2) is not included in the solution set.

For (1,-5)

`4(1)+(-5)>3\Rightarrow -1>3` False

So, (1,-5) is not included in the solution set.

For (0,0)

`4(0)+(0)>3\Rightarrow 0>3` False

So, (0,0) is not included in the solution set.

For (5,-2)

`4(5)+(-2)>3\Rightarrow 18>3` True

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

Both inequalities are true for the point (5,-2). So, the point (5,-2) is a solution for the following system of inequalities

Therefore, the correct option is D.