Try the fastest way to create flashcards
Question

# How can you tell whether an ordered pair is a solution of a linear inequality?

Solution

Verified
Step 1
1 of 2

To verify this statement you can substitute the pair at both sides of the inequality. The inequality holds for this pair if and only if the pair is one of its solutions. For example, let us consider the inequality

$y \geq 2 x-1$

The pair $(0,0)$ is a solution of the inequality, because

\begin{align*} y &\geq 2 x-1 && \text {Write the inequality } \\ 0 &\stackrel{?}{\geq} 2(0)-1 && \text {Replace } x \text { and } y \text { by } 0 \\ 0 & \geq-1&&\text{True conclusion} \end{align*}

Nevertheless, $(0,2)$ is not a solution of the inequality, because

\begin{align*} y &\geq 2 x-1&&\text {Write the inequality } \\ 0 &\stackrel{?}{\geq}2(2)-1&& \text {Replace } x \text { by } 0 \text{ and }y \text { by }2 \\ 0 &\geq 3&&\text{False conclusion} \end{align*}

## Recommended textbook solutions #### enVision Algebra 1

1st EditionISBN: 9780328931576Al Cuoco, Christine D. Thomas, Danielle Kennedy, Eric Milou, Rose Mary Zbiek
3,653 solutions #### Algebra 1

4th EditionISBN: 9781602773011Saxon
5,377 solutions #### Big Ideas Math Algebra 1: A Common Core Curriculum

1st EditionISBN: 9781608408382Boswell, Larson
4,740 solutions #### Big Ideas Math Integrated Mathematics II

1st EditionISBN: 9781680330687Boswell, Larson
4,539 solutions