Question

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

Answer 1

Answer:

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

Step-by-step 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)