## Related questions with answers

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

Solution

VerifiedTo 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

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

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