Question

Consider the following system of inequalities below.

Answer 1

Option A, B, C

(-4, -3) and (1, 6) and (2, 4) is a solution to given system of inequalities

Solution:

Given system of inequalities are:

Line 1 : 3y < 2x + 18

Line 2 : -4y < -x + 12

Let us substitute the given solution set in options and check if it satisfies both the inequalities

Option A

Substitute x = -4 and y = -3 in Line 1

$3(-3) < 2(-4) + 18\\\\-9$

-9 less than 10 is true

Substitute x = -4 and y = -3 in Line 2

$-4(-3) < -(-4) + 12\\\\12$

12 less than 16 is true

Thus (-4, -3) is a solution to given system of inequalities

Option B

Substitute x = 1 and y = 6 in line 1

$3(6)$

18 less than 20 is true

Substitute x = 1 and y = 6 in line 2

$-4(6) < -(1) + 12\\\\-24$

-24 is less than 11 is true

Thus (1, 6) is a solution to given system of inequalities

Option C

Substitute x = 2 and y = 4 in line 1

$3(4)$

12 is less than 22 is true

Substitute x = 2 and y = 4 in line 2

$-4(4)$

-16 less than 10 is true

So, (2, 4) is a solution to given system of inequalities

Option D

Substitute x = 5 and y = -5 in line 1

$3(-5)$

-15 is less than 28 is true

Substitute x = 5 and y = -5 in line 2

$-4(-5)$

20 less than 7 is not true

Thus (5, -5) is not a solution to given system of inequalities

Option E

Substitute x = 3 and y = 2 in line 1

$3(2)$

6 less than 24 is not true

Thus (3, 2) is not a solution to given system of inequalities