Respuesta :

texaschic101
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:

Option D.

Step-by-step explanation:

The given system of inequalities are

[tex]4x+y>3[/tex]

[tex]x-y>2[/tex]

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

Check each point by these inequalities.

For (-2,-2)

[tex]4(-2)+(-2)>3\Rightarrow -10>3[/tex] False

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

For (1,-5)

[tex]4(1)+(-5)>3\Rightarrow -1>3[/tex] False

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

For (0,0)

[tex]4(0)+(0)>3\Rightarrow 0>3[/tex] False

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

For (5,-2)

[tex]4(5)+(-2)>3\Rightarrow 18>3[/tex] True

[tex](5)-(-2)>2\Rightarrow 7>2[/tex] 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.

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