Question

6 which ordered pair is a solution to the system of inequalities shown?
$5x + 3y \geq 6$
$4x - 3y \geq 21$
a) (5, -3) las vegas
b) (0, 6) new york city
c) (-4, -9) dallas
d) (-1, 2) chicago
e) (-8, 0) san francisco

Explanation:

Step1: Test option A (5,-3) in first inequality

$5(5) + 3(-3) = 25 - 9 = 16 \geq 6$ (true)

Step2: Test option A in second inequality

$4(5) - 3(-3) = 20 + 9 = 29 \geq 21$ (true)

Step3: Verify other options (example B: (0,6))

First inequality: $5(0)+3(6)=18\geq6$ (true); Second: $4(0)-3(6)=-18\geq21$ (false)

Step4: Confirm only A satisfies both

Only (5,-3) makes both inequalities true.

Answer:

A) (5, -3) Las Vegas