Question

Which ordered pairs are in the solution set of the system of linear inequalities?

Answer 1

Thought Process:

The solution to this can be found through plotting both of these functions and shading each region above or below the lines (as per the greater and less than signs given)

the region that overlaps both of the above shaded region is the solution set for all ordered pairs that satisfy the two inequalities.

Solution:

let's start by plotting

$y > -\dfrac{1}{3}x + 2$

it's the same as plotting $y = -\dfrac{1}{3}x + 2$, but '>' sign suggests to shade everything above this line.

side note:

'$>$' excludes every ordered pair in the line,

'$\leq$' includes every ordered pair in the line,

coming back to our solution:

now let's plot the other equation

$y > 2x + 3$

it's the same as plotting  $y = 2x + 3$, but '<' sign suggests to shade the area below this line.

The solution set is the area that is overlapped by the two shaded regions.

So every ordered pair (or coordinate (x,y)) that lies within this overlapped shaded region, excluding the points that lie on the lines themselves, satisfy the given two inequalities

Answer 2

Answer:

Your answer is A) - (2, 2), (3, 1), (4, 2)

Step-by-step explanation:

I hope this helps!

- sincerelynini