Which ordered pairs is a solution to −5x + 3y > 12? (3, 9)

(-5, 5)

(3, -6)

(-2, -5)

(2, 8)

(-6, 0)

Answer :-

Given inequality ,

-5x +3y > 12 3y > 5x + 12 y > 5/3x + 12/3y > 5/3x + 4

From the options ,

When x is 3 and y = 9

y >1* 5 + 4y > 5 +4 9> 9 ( Not possible )

When x is -5 y is 5

y > 5/3*-5 + 4y > -8.3 + 4 5 > -3.7 ( Possible )

When x is 3 y is -6

y > 5 + 4 -6 > 9 ( Not possible )

When x is -2 y is -5

y > -3.33 + 4 -5 > -0.67 ( Possible )

When x is 2 y is 8

y > 3.33 + 4 8 > 7.77 ( possible )

When x is -6 y is 0

y > -10 +4 0 > -6 ( possible )

Given the inequality statement, -5x + 3y > 12

We’ll substitute the given points to determine which is a solution that satisfies the inequality:

(3, 9):
-5(3) + 3(9) > 12
-15 + 27 > 12
12 > 12 (False statement, as 12 ≯ 12)

(-5, 5):

-5x + 3y > 12

-5(-5) + 3(5) > 12

25 + 15 > 12

40 > 12 (True statement). Thus, it is a solution.

(3, -6)
-5(3) + 3(-6) > 12
-15 - 18 > 12
-33 > 12 (False statement. -33 ≯ 12).

(-2, -5)
-5(-2) + 3(-5) > 12
10 - 15 > 12
-5 > 12 (False statement. -5 ≯ 12).

Therefore, the only solution is (-5, 5).

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