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Chapter 3: Problem 51

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

Short Answer

Expert verified
A linear inequality in two variables is a statement about a region of the coordinate plane comprising all solutions to the inequality. It can be written as \( ax + by > c \), \( ax + by < c \), \( ax + by \geq c \), or \( ax + by \leq c \). An example is \(2x + 3y > 6 \)

Step by step solution

01

Define Linear Inequality

A linear inequality in two variables is a statement that represents a region of the coordinate plane that includes all solutions to the inequality. The simplest form of it can be written as \( ax + by > c \), \( ax + by < c \), \( ax + by \geq c \), or \( ax + by \leq c \), where \( a \), \( b \), and \( c \) are constants, and \( x \) and \( y \) are variables. The inequality symbol can be , < , > , 鈮� , or 鈮�.
02

Provide an Example

An example of a linear inequality in two variables is \(2x + 3y > 6 \). The solution set for this inequality is a half-plane made of points that satisfy the inequality. Hence any solution can be a point \( (x, y) \) in this half-plane.

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Most popular questions from this chapter

Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities in $$y \geq \frac{1}{2} x+4$$

Will help you prepare for the material covered in the first section of the next chapter. Is \((4,-1)\) a solution of both \(x+2 y=2\) and \(x-2 y=6 ?\)

Will help you prepare for the material covered in the first section of the next chapter. Is \((-4,3)\) a solution of both \(x+2 y=2\) and \(x-2 y=6 ?\)

determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. The graph that I'm looking at is U-shaped, so its equation cannot be of the form \(y=m x+b\)

Graph equation. \(5 y=20\)
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