59.1k views
3 votes
Which system of inequalities has the solution region shown in the graph below?

Which system of inequalities has the solution region shown in the graph below?-example-1
User Disperse
by
8.4k points

1 Answer

3 votes

The system of inequalities in the graph is:

y ≥ x

y > (-2/3)*x + 2

How to find the system?

Here we have a system of linear inequalities, so we need to find both inequalities.

First we can see a solid line with positive slope, we can see taht the shaded area is above the line, then we can write:

y ≥ line

Now, this line intercepts the y-axis at y = 0, and for each unit that we move to the right we move one unit up, so the line is y = x, then the inequality is:

y ≥ x

Then we can see that the other inequality is a dashed line, again, the shaded region is above the line:

y > ax + b

Here the y-intercept is y = 2

y > ax + 2

And it passes through (3, 0), then:

0 = a*3 + 2

-2 = a*3

-2/3 = a

This inequality is:

y > (-2/3)*x + 2

The system is:

y ≥ x

y > (-2/3)*x + 2

User Geezer
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories