Which Of The Following Is A Solution Of $y-x\ \textgreater \ -3$?A. \[$(2,6)\$\]B. \[$(2,-1)\$\]C. \[$(6,2)\$\]

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Introduction

In mathematics, solving inequalities is a crucial concept that helps us understand the relationship between variables. When dealing with linear inequalities, we need to find the values of the variables that satisfy the given inequality. In this article, we will explore the solution to the inequality y−x \textgreater −3y-x\ \textgreater \ -3 and determine which of the given options is a solution.

Understanding the Inequality

The given inequality is y−x \textgreater −3y-x\ \textgreater \ -3. To solve this inequality, we need to isolate the variable yy. We can do this by adding xx to both sides of the inequality, which gives us y \textgreater x−3y\ \textgreater \ x-3. This means that the value of yy must be greater than x−3x-3.

Analyzing the Options

We are given three options to choose from:

A. {(2,6)$}$ B. {(2,-1)$}$ C. {(6,2)$}$

To determine which of these options is a solution, we need to substitute the values of xx and yy into the inequality and check if it is true.

Option A: {(2,6)$}$

For option A, we have x=2x=2 and y=6y=6. Substituting these values into the inequality, we get:

6−2 \textgreater −36-2\ \textgreater \ -3

Simplifying the inequality, we get:

4 \textgreater −34\ \textgreater \ -3

This is true, so option A is a solution to the inequality.

Option B: {(2,-1)$}$

For option B, we have x=2x=2 and y=−1y=-1. Substituting these values into the inequality, we get:

−1−2 \textgreater −3-1-2\ \textgreater \ -3

Simplifying the inequality, we get:

−3 \textgreater −3-3\ \textgreater \ -3

This is not true, so option B is not a solution to the inequality.

Option C: {(6,2)$}$

For option C, we have x=6x=6 and y=2y=2. Substituting these values into the inequality, we get:

2−6 \textgreater −32-6\ \textgreater \ -3

Simplifying the inequality, we get:

−4 \textgreater −3-4\ \textgreater \ -3

This is not true, so option C is not a solution to the inequality.

Conclusion

In conclusion, the only option that is a solution to the inequality y−x \textgreater −3y-x\ \textgreater \ -3 is option A: {(2,6)$}$. This is because when we substitute the values of xx and yy into the inequality, we get a true statement.

Frequently Asked Questions

  • What is the solution to the inequality y−x \textgreater −3y-x\ \textgreater \ -3?
  • How do we determine which option is a solution to the inequality?
  • What is the relationship between the variables xx and yy in the inequality?

Final Answer

The final answer is option A: {(2,6)$}$.

Introduction

In our previous article, we explored the solution to the inequality y−x \textgreater −3y-x\ \textgreater \ -3 and determined which of the given options is a solution. In this article, we will answer some frequently asked questions related to solving inequalities.

Q&A

Q: What is the solution to the inequality y−x \textgreater −3y-x\ \textgreater \ -3?

A: The solution to the inequality y−x \textgreater −3y-x\ \textgreater \ -3 is any point that lies above the line y=x−3y=x-3. This means that the value of yy must be greater than x−3x-3.

Q: How do we determine which option is a solution to the inequality?

A: To determine which option is a solution to the inequality, we need to substitute the values of xx and yy into the inequality and check if it is true. If the statement is true, then the option is a solution.

Q: What is the relationship between the variables xx and yy in the inequality?

A: In the inequality y−x \textgreater −3y-x\ \textgreater \ -3, the variable yy is greater than the variable xx minus 3. This means that the value of yy must be greater than the value of xx minus 3.

Q: How do we solve linear inequalities?

A: To solve linear inequalities, we need to isolate the variable on one side of the inequality. We can do this by adding or subtracting the same value from both sides of the inequality, or by multiplying or dividing both sides of the inequality by the same non-zero value.

Q: What is the difference between a linear inequality and a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, 2x+3=52x+3=5 is a linear equation. A linear inequality, on the other hand, is an inequality in which the highest power of the variable is 1. For example, 2x+3>52x+3>5 is a linear inequality.

Q: How do we graph linear inequalities?

A: To graph a linear inequality, we need to graph the corresponding linear equation and then shade the region that satisfies the inequality. If the inequality is of the form y>xy>x, we shade the region above the line. If the inequality is of the form y<xy<x, we shade the region below the line.

Q: What is the significance of solving linear inequalities?

A: Solving linear inequalities is important in many real-world applications, such as finance, economics, and engineering. For example, in finance, we may need to determine the maximum or minimum value of an investment based on certain conditions. In economics, we may need to determine the optimal price of a product based on demand and supply. In engineering, we may need to determine the maximum or minimum value of a physical quantity, such as stress or strain.

Conclusion

In conclusion, solving linear inequalities is an important concept in mathematics that has many real-world applications. By understanding how to solve linear inequalities, we can make informed decisions in various fields, such as finance, economics, and engineering.

Final Answer

The final answer is that solving linear inequalities is an important concept in mathematics that has many real-world applications.