Answer:
(3, -8) and (2, -10)
Step-by-step explanation:
Given
[tex]10x + 4y < 12[/tex]
[tex]8x - 3y > 20[/tex]
Required
Select the true coordinate points in (3, -8) (2, 5) (-5, 1) (10, 3) (2, -10)
(3, -8)
x = 3 and y = -8
[tex]10x + 4y < 12[/tex]
[tex]10 * 3 + 4 * -8 < 12[/tex]
[tex]30 - 32 < 12[/tex]
[tex]-2 < 12[/tex] --- True
[tex]8x - 3y > 20[/tex]
[tex]8 * 3 - 3 * -8> 20[/tex]
[tex]24 +24> 20[/tex]
[tex]48> 20[/tex] --- True
(2, 5)
x = 2 and y = 5
[tex]10x + 4y < 12[/tex]
[tex]10 * 2 + 4 * 5 < 12[/tex]
[tex]20 + 20 < 12[/tex]
[tex]40 < 12[/tex] --- False (No need to check the other inequality)
(-5, 1)
x = -5 and y = 1
[tex]10x + 4y < 12[/tex]
[tex]10 * -5 + 4 * 1 < 12[/tex]
[tex]-46 < 12[/tex] --- True
[tex]8x - 3y > 20[/tex]
[tex]8 * -5 - 3 * 1 > 20[/tex]
[tex]-43 > 20[/tex] --- False
(10, 3)
x = 10 and y = 3
[tex]10x + 4y < 12[/tex]
[tex]10 * 10 + 4 * 3 < 12[/tex]
[tex]112 < 12[/tex] --- False (No need to check the other inequality)
(2, -10)
x = 2 and y = -10
[tex]10x + 4y < 12[/tex]
[tex]10 * 2 + 4 * -10 < 12[/tex]
[tex]-20 < 12[/tex] --- True
[tex]8x - 3y > 20[/tex]
[tex]8 * 2 - 3 * -10 > 20[/tex]
[tex]46 > 20[/tex] --- True
Hence, the solution to the inequalities are:
(3, -8) and (2, -10)
