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Video: Identifying Regions That Represent the Solutions to a System of Inequalities

Bethani Gasparine

Which regions on the graph contain solutions to both of the following inequalities? y& > -x-4 y &β‰₯ 2x-4<Figure>

01:08

Video Transcript

Which regions on the graph contain solutions to both of the following inequalities? 𝑦 is greater than negative π‘₯ minus four and 𝑦 is greater than or equal to two π‘₯ minus four.

Notice both of these inequalities have 𝑦-intercepts at negative four, so they cross the 𝑦-axis at negative four.

Now, the first inequality has a negative slope and it also has a greater than sign, which means it should have a dashed line. So here, we have our first line. Now, when it says that it’s greater than, then we should shade everything above that line, which we’ll denote with arrows.

Now our other inequality has a positive slope of two and a greater than or equal to sign, so we should have a solid line and we should shade everything above that. So our solution will be where both of these inequalities overlap, and we can see that here. So the regions would be 𝐴 and 𝐷.