Problem 114 - College Algebra

Question

Write a system of inequalities whose solution set includes every point in the rectangular coordinate system.

Step-by-Step Solution

Answer

The system of inequalities that includes every point in the rectangular coordinate system is: \(x \geq -\infty, x \leq \infty, y \geq -\infty, y \leq \infty \).

Step 1: Understand the Rectangular Coordinate System

A rectangular coordinate system is a plane with two perpendicular lines intersecting at their midpoints. These lines are usually called x-axis and y-axis. Each point on this plane can be represented as a pair of numbers (x, y), signifying the distance of the point from zero along each axis.

Step 2: Identify Universal Inequalities

In order to include every point in the rectangular coordinate system, the inequalities should be universal for every possible value of x and y. By considering the nature of the rectangular coordinate system where x and y are ranging from negative infinity to positive infinity we can write down four universal inequalities to include every point in the plane: \(x \geq -\infty, x \leq \infty, y \geq -\infty, y \leq \infty \). These inequalities include all points in the rectangular coordinate system.

Step 3: Formulate the System of Inequalities

Judging from the above analysis, it is clear that the system of inequalities that will satisfy the condition is \(x \geq -\infty, x \leq \infty, y \geq -\infty, y \leq \infty \). This system will include every possible point in the rectangular system.