Question

1. # Which System Of Linear Inequalities Has The Point (3, –2) In Its Solution Set?

## Introduction

Linear inequalities are mathematical equations that involve the comparison of two expressions. They are used to compare the value of a variable to a constant and can have multiple solutions. In this article, we will look at which system of linear inequalities has the point (3, -2) in its solution set. We will also discuss how to use systems of linear inequalities to solve real-world problems. Read on to learn more about linear inequalities and their applications in mathematics!

## What is a Linear Inequality?

A linear inequality is an mathematical statement that defines a range of values that a variable can take. It is usually written in the form of “y < x + 3” or “x > 2”. The first example defines all the y values that are less than x+3, while the second example defines all the x values that are greater than 2.

## What is the Solution Set?

The solution set for a system of linear inequalities is the set of points that satisfy all the inequalities in the system. In this case, the point (, –) satisfies all the inequalities in the system, so it is in the solution set.

## The Point (3, -2)

The point (3, -2) is in the solution set of the system of linear inequalities below:

{ y > -2x + 3

y < 2x – 3

y < -x + 3

y > x – 3 }

## Conclusion

In conclusion, we have determined that the point (3,-2) is in the solution set of the system of linear inequalities y ≤ –x + 4 and y ≥ x – 7. We used our knowledge of graphing inequalities on a coordinate plane to identify solutions for each equation separately, then overlapped them to arrive at our final answer. With this understanding in hand, you will be well equipped to solve similar problems involving linear equations and their solution sets.

2. Have you ever wondered which system of linear inequalities has a certain point in its solution set? If so, then you’ve come to the right place!

In this blog post, we’ll look at the system of linear inequalities that has the point (3, -2) in its solution set. This is a great example of how a system of linear inequalities can be used to solve a problem.

But first, let’s go over some of the basics. A linear equation is an equation that can be written in the form of ax + by = c, where a, b and c are real numbers, and x and y are variables. A system of linear inequalities is a set of linear equations that have an equal sign between them.

Now that we understand what a system of linear inequalities is, let’s take a look at the point (3, -2) and how it fits into the system of linear inequalities.

To find the solution set of a system of linear inequalities with the point (3, -2) in it, we need to solve the following equation:

-2x + 3y ≤ 0

This equation can be rearranged to:

-2x + 3y ≤ 0

y ≤ -2/3x

This equation tells us that for any value of x, the corresponding value of y must be less than or equal to -2/3x. So if we plug in x = 3, then the corresponding value of y must be less than or equal to -2.

Therefore, the system of linear inequalities that has the point (3, -2) in its solution set is:

-2x + 3y ≤ 0

y ≤ -2/3x

Now that we know which system of linear inequalities has the point (3, -2) in its solution set, let’s take a moment to think about the implications of this.

Linear equations and systems of linear inequalities are important tools in mathematics and can be used to solve many different types of problems. They can also be used to understand the relationships between different numbers and variables.

So, if you’re ever wondering which system of linear inequalities has a certain point in its solution set, hopefully this blog post has provided some insight!