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

Question Video: Identifying Regions That Represent the Solutions to a System of Inequalities Mathematics • First Year of Secondary School

Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

Which region on the graph contains solutions to the set of inequalities 𝑦 < 2, 𝑦 ≥ −𝑥, 𝑥 < 1?

02:37

Video Transcript

Which region on the graph contains solutions to the set of inequalities 𝑦 is less than two, 𝑦 is greater than or equal to negative 𝑥, and 𝑥 is less than one?

In order to answer this question, we begin by considering what the graphs of the equations 𝑦 equals two, 𝑦 equals negative 𝑥, and 𝑥 equals one would look like. Any equation 𝑦 equals some constant 𝑎 will correspond to a horizontal line. The equation 𝑦 equals two will, therefore, be a horizontal line passing through two on the 𝑦-axis. We draw this as a broken line, as the inequality is strictly less than. In a similar way, any equation of the form 𝑥 equals 𝑎, where 𝑎 is some constant, will be a vertical line. The equation 𝑥 equals one corresponds to a vertical line passing through one on the 𝑥-axis. Once again, this is a broken line, as the inequality sign is strictly less than.

We know that any point that lies on the equation 𝑦 equals negative 𝑥 will have a 𝑦-coordinate equal to the negative of the 𝑥-coordinate. For example, the points two, negative two and one, negative one lie on the line 𝑦 equals negative 𝑥. The points negative one, one and negative two, two will also lie on this line. This line 𝑦 equals negative 𝑥 also passes through the origin as shown.

Now that we’ve drawn the lines of these three equations, we need to consider the region that satisfies the inequalities. Firstly, 𝑦 is less than two. Therefore, our region must lie below the line 𝑦 equals two. In a similar way, 𝑥 is less than one. Therefore, our region must lie to the left of 𝑥 equals one. Finally, we have 𝑦 is greater than or equal to negative 𝑥. This means that our region must lie above the line 𝑦 equals negative 𝑥. The region that satisfies all three of these inequalities is therefore region A.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy