Problem 87 - College Algebra Essentials

Question

What is a linear inequality in two variables? Provide an example with your description.

Step-by-Step Solution

Answer

A linear inequality in two variables can be written in the form of \(Ax + By > C\), \(Ax + By < C\), \(Ax + By \geq C\), or \(Ax + By \leq C\), where A, B and C are real numbers, and A and B are not both zero. For instance, \(3x + 2y \geq 6\) is an example of a linear inequality in two variables.

Step 1: Define Linear Inequality in Two Variables

A linear inequality in two variables is an inequality that involves linear expressions in two variables. This inequality can be written in the form of \( Ax + By > C \), \( Ax + By < C \), \( Ax + By \geq C \), or \( Ax + By \leq C \), where A, B, and C are real numbers and A and B are not both zero.

Step 2: Provide an Example

For example, consider the inequality \( 3x + 2y \geq 6 \). This is a linear inequality in two variables, where A = 3, B = 2 and C = 6. This inequality includes all points \((x, y)\) that make the inequality true when \(x\) and \(y\) are substituted into the inequality.