Question

2 which ordered pair is a solution to the system of inequalities shown?
$7x + 3y \geq 6$
$x - y \leq 8$
a) (1, -4) elated
b) (8, -3) overwhelmed
c) (-5, 6) nervous
d) (0, -1) enthusiastic
e) (4, 5) tickled pink

Explanation:

Step1: Test option A (1,-4)

First inequality: $7(1)+3(-4)=7-12=-5 < 6$ → fails.

Step2: Test option B (8,-3)

First inequality: $7(8)+3(-3)=56-9=47 ≥6$; Second inequality: $8-(-3)=11 >8$ → fails.

Step3: Test option C (-5,6)

First inequality: $7(-5)+3(6)=-35+18=-17 <6$ → fails.

Step4: Test option D (0,-1)

First inequality: $7(0)+3(-1)=-3 <6$ → fails.

Step5: Test option E (4,5)

First inequality: $7(4)+3(5)=28+15=43 ≥6$; Second inequality: $4-5=-1 ≤8$ → passes.

Answer:

E) (4, 5)