Question

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

y > -1/3x+ 2

y < 2x+3

Answer 1

The solution set of the given system of linear inequalities consists of ordered pairs that satisfy both y > -1/3x + 2 and y < 2x + 3, which can be found by graphing the inequalities and identifying the overlapping shaded region.

Step-by-step explanation:

To determine which ordered pairs are part of the solution set for the given system of linear inequalities, we need to look at the constraints provided by each inequality.

• 
  
• y > -1/3x + 2 implies that the solution lies above the line y = -1/3x + 2.
• 
  
• y < 2x + 3 implies that the solution lies below the line y = 2x + 3.

Any ordered pair that satisfies both conditions will be in the solution set. To find these, you may graph the inequalities on a coordinate plane and look at the overlapping region. The solution set will be the intersection of the shaded areas above the first line and below the second line.

Answer 2

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 > -(1)/(3)x + 2`

it's the same as plotting
`y = -(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