Answer
Option D is the answer.
Point (-10, -7) is not a solution to the system of lineare inequalities.
Step-by-step explanation
The inequalities to be examined include
y < (4x/5) - 2
And
y > -3x + 7
We are now asked to evaluate if a couple of answers satisfy the two inequalities
(5, -5)
x = 5, y = -5
y < (4x/5) - 2
Inserting the numbers
-5 < (4×5/5) - 2
-5 < 4 - 2
-5 < 2
This is true
y > -3x + 7
Inserting the numbers
-5 > -3 (5) + 7
-5 > -15 + 7
-5 > -8
This is also true.
(5, -5) is a solution for the system of inequalities.
(5, -6)
x = 5, y = -6
y < (4x/5) - 2
Inserting the numbers
-6 < (4×5/5) - 2
-6 < 4 - 2
-6 < 2
This is true
y > -3x + 7
Inserting the numbers
-6 > -3 (5) + 7
-6 > -15 + 7
-6 > -8
This is also true.
(5, -6) is a solution for the system of inequalities.
(10, -8)
x = 10, y = -8
y < (4x/5) - 2
Inserting the numbers
-8 < (4×10/5) - 2
-8 < 8 - 2
-8 < 6
This is true
y > -3x + 7
Inserting the numbers
-8 > -3 (10) + 7
-8 > -30 + 7
-8 > -23
This is also true.
(10, -8) is a solution for the system of inequalities.
(-10, -7)
x = -10, y = -7
y < (4x/5) - 2
Inserting the numbers
-7 < (4×-10/5) - 2
-7 < -8 - 2
-7 < -10
This is not true
y > -3x + 7
Inserting the numbers
-7 > -3 (-10) + 7
-7 > 30 + 7
-7 > 37
This is also not true.
(-10, -7) is not a solution for the system of inequalities.
Hope this Helps!!!