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Is the ordered pair a solution to the given inequality? $$9 x-2 y<-1 ;(-1,-3)$$

Short Answer

Expert verified
Yes, the ordered pair \((-1,-3)\) is a solution to the inequality.

Step by step solution

01

Understand the inequality

First, identify the given inequality which needs to be tested with the ordered pair \((-1,-3)\). The inequality is \(9x - 2y < -1\). Each ordered pair consists of two values: \(x\) and \(y\). In this case, \(x=-1\) and \(y=-3\).
02

Substitute the ordered pair into the inequality

Replace \(x\) with \(-1\) and \(y\) with \(-3\) in the inequality. This gives us \(9(-1) - 2(-3) < -1\).
03

Simplify the left-hand side of the inequality

Calculate \(9(-1)\) which equals \(-9\) and calculate \(-2(-3)\) which equals \(6\). Therefore, the inequality becomes \(-9 + 6 < -1\).
04

Perform the addition

Add \(-9\) and \(6\) to get \(-3\). The inequality now reads \(-3 < -1\).
05

Determine whether the inequality holds

Check if \(-3 < -1\). Since \(-3\) is indeed less than \(-1\), the inequality holds true with the given values.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ordered Pairs
Ordered pairs are like coordinates on a map—they tell us where a point is located in a two-dimensional space. They are written in the form \( (x, y) \) where \( x \) is the first value and \( y \) is the second value. In our exercise, we have the ordered pair \( (-1, -3) \). Here, \( -1 \) is the value of \( x \) and \( -3 \) is the value of \( y \).

To use ordered pairs in an inequality, you substitute the values of \( x \) and \( y \) from the pair into the inequality equation. This gives you a way to check if the whole equation or inequality is true for this particular pair of numbers.

An important note: ordered pairs are direction-sensitive. This means \( (x, y) \) is not the same as \( (y, x) \)."},{

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