Question

Consider the system of inequalities.

3x + 2y < 8
-5x - 9y > -2
Select all ordered pairs that are solutions to the system of inequalities.
(-10, -3)
a)
b)
(-1, 5)
(0, 0)
d)
(1, -1)

Answer 1

b)

The point is (-1,5) and (0,0) also satisfies the given inequalities

The solution of the given inequalities

(x, y) = (4 , -2 )

Explanation:

Step(i):-

Given system of equations are

3x + 2y < 8

-5x - 9y > -2

The solution of the given equations are

3x + 2y = 8 multiply '5'

-5x - 9y = -2 multiply '3'

15 x + 10 y = 40 ...(i)

-15x - 27 y = -6.....(ii)

Adding (i) and (ii) , we get

- 17 y = 34

y = -2

Substitute y = -2 in equation 3x + 2y =8

3x - 4 =8

3x = 12

x =4

The solution of the given system of inequalities

(x, y) = (4 , -2 )

Step(ii):-

3x + 2y < 8

-5x - 9y > -2

The point is (-1,5)

-3 + 10 < 8

7 < 8

5 - 45 > -2

-40 > -2

The point (0,0) also satisfies the given inequalities

Final answer :-

The point is (-1,5) and (0,0) also satisfies the given inequalities