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Chapter 5: Problem 87

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

Short Answer

Expert verified
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 by step solution

01

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.
02

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.

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Most popular questions from this chapter

write the partial fraction decomposition of each rational expression. $$ \frac{3 x-5}{x^{3}-1} $$

Solve by the addition method: $$ \left\\{\begin{array}{l} 2 x+4 y=-4 \\ 3 x+5 y=-3 \end{array}\right. $$

Describe in general terms how to solve a system in three variables.

will help you prepare for the material covered in the next section. Solve by the substitution method: $$ \left\\{\begin{array}{l} 4 x+3 y=4 \\ y=2 x-7 \end{array}\right. $$

Solve the system: $$\left\\{\begin{aligned} x+y+2 z &=19 \\ y+2 z &=13 \\ z &=5 \end{aligned}\right.$$ What makes it fairly easy to find the solution?
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