Problem 114 - College Algebra Essentials

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 \(x \leq ∞\), \(x \geq -∞\), \(y \leq ∞\), and \(y \geq -∞\).

Step 1: Understand the Rectangular Coordinate System

The rectangular coordinate system includes all points with x and y coordinates that range from -∞ to +∞. This means that any point in the rectangular coordinate system can be represented as (x, y), where x and y can be any real numbers.

Step 2: Formulate the Inequalities

Based on the definition of the rectangular coordinate system, the applicable inequalities can be \(x \leq ∞\), \(x \geq -∞\), \(y \leq ∞\), and \(y \geq -∞\). Any point in the rectangular coordinate system will satisfy these conditions.

Step 3: Combine the Inequalities

Combining these inequalities together would generate the system of inequalities: \(x \leq ∞\), \(x \geq -∞\), \(y \leq ∞\), \(y \geq -∞\). These inequalities cover every point in the rectangular coordinate system. Moreover, due to the unbounded nature of values, the graph depicting this will incorporate both positive and negative infinites for x and y.