Question

Select all of the points that are solutions to the system of linear inequalities that is listed below 10x + 4y < 12 8x -3y > 20

Answer 1

(3, -8) and (2, -10)

Explanation:

Given

`10x + 4y < 12`

`8x - 3y > 20`

Required

Select the true coordinate points in (3, -8) (2, 5) (-5, 1) (10, 3) (2, -10)

(3, -8)

x = 3 and y = -8

`10x + 4y < 12`

`10 * 3 + 4 * -8 < 12`

`30 - 32 < 12`

`-2 < 12` --- True

`8x - 3y > 20`

`8 * 3 - 3 * -8> 20`

`24 +24> 20`

`48> 20` --- True

(2, 5)

x = 2 and y = 5

`10x + 4y < 12`

`10 * 2 + 4 * 5 < 12`

`20 + 20 < 12`

`40 < 12` --- False (No need to check the other inequality)

(-5, 1)

x = -5 and y = 1

`10x + 4y < 12`

`10 * -5 + 4 * 1 < 12`

`-46 < 12` --- True

`8x - 3y > 20`

`8 * -5 - 3 * 1 > 20`

`-43 > 20` --- False

(10, 3)

x = 10 and y = 3

`10x + 4y < 12`

`10 * 10 + 4 * 3 < 12`

`112 < 12` --- False (No need to check the other inequality)

(2, -10)

x = 2 and y = -10

`10x + 4y < 12`

`10 * 2 + 4 * -10 < 12`

`-20 < 12` --- True

`8x - 3y > 20`

`8 * 2 - 3 * -10 > 20`

`46 > 20` --- True

Hence, the solution to the inequalities are:

(3, -8) and (2, -10)