374,824 views
18 votes
18 votes
Which point would not be a solution to the system of linear inequalities shown below? y<4/5x-2. y>-3x+7 answers: (5,-5)(5,-6)(10,-8)(-10,-7)

User Mahmut EFE
by
3.0k points

1 Answer

16 votes
16 votes

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!!!

User Hugemeow
by
2.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.