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For the following inequalities in two variables, pick any THREE ordered pairs to determine if they lie in the solution space or not.

14 viewed last edited 5 months ago
Anonymous
0

y \gt 3 x-11


a. Test point #1:


Is it part of the solution space? _________


b. Test point #2:


Is it part of the solution space? _________


c. Test point #3:


Is it part of the solution space? ______



Sangeetha Pulapaka
1

Step 1:

Recall what an ordered pair is . An ordered pair is written in the form (x, y) where x is the x-coordinate and y is the y-coordinate.

Step 2:

Recall what a solution is. A solution is the set of ordered pairs which satisfy the linear equation or linear inequality.

Recall what is a solution pace is. A solution space is where the solution of the inequality lies in.

  y > 3 x-11

Consider (0,0) to be the first test point. Plug in x = 0 and y = 0 in the inequality

y  > 3 x -11 we get

0  > 0 - 11

Since 0 > -11 (0,0) is a part of the solution space. This is test point #1

Step 3:

Plug in a set of different ordered pairs to check if the ordered pair lies in the solution space or not.

Plug in (-1,5) in y > 3 x - 1

we get 5 > 3(-1) - 1

            5 > -4

So (-1,5) lies in the solution space and this is test point #2

Step 4:

Plug in a set of different ordered pair to check if this ordered pair lies in the solution space or not.

Plug in (1,1) in the inequality y > 3 x - 11

1 > 3 - 11

1 > -8

So (1,1) lies in the solution space and this is test point #3