If X Y = 4 \frac{x}{y}=4 Y X ​ = 4 And 24 X N Y = 4 \frac{24x}{ny}=4 N Y 24 X ​ = 4 , What Is The Value Of N N N ? □ \square □

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Introduction

In this article, we will explore a system of equations involving fractions and solve for the value of a variable, n. The given equations are xy=4\frac{x}{y}=4 and 24xny=4\frac{24x}{ny}=4. Our goal is to find the value of n that satisfies both equations.

Understanding the Given Equations

The first equation, xy=4\frac{x}{y}=4, tells us that the ratio of x to y is equal to 4. This means that x is 4 times y, or x = 4y.

The second equation, 24xny=4\frac{24x}{ny}=4, involves a more complex expression. We can simplify this equation by multiplying both sides by ny, which gives us 24x = 4ny.

Simplifying the Second Equation

To simplify the second equation, we can divide both sides by 4, which gives us 6x = ny.

Equating the Two Expressions for x

We can now equate the two expressions for x: 4y = 6x. Since we know that x = 4y, we can substitute this expression into the equation 6x = ny, which gives us 6(4y) = ny.

Solving for n

Simplifying the equation 6(4y) = ny, we get 24y = ny. To solve for n, we can divide both sides by y, which gives us n = 24.

Conclusion

In this article, we have solved a system of equations involving fractions to find the value of n. By simplifying the second equation and equating the two expressions for x, we were able to solve for n. The value of n is 24.

Step-by-Step Solution

Here is a step-by-step solution to the problem:

  1. Start with the given equations: xy=4\frac{x}{y}=4 and 24xny=4\frac{24x}{ny}=4.
  2. Simplify the first equation to get x = 4y.
  3. Simplify the second equation to get 6x = ny.
  4. Equate the two expressions for x: 4y = 6x.
  5. Substitute x = 4y into the equation 6x = ny to get 6(4y) = ny.
  6. Simplify the equation 6(4y) = ny to get 24y = ny.
  7. Divide both sides of the equation 24y = ny by y to get n = 24.

Final Answer

Introduction

In our previous article, we solved a system of equations involving fractions to find the value of n. In this article, we will answer some frequently asked questions (FAQs) about solving for n in a system of equations.

Q: What is the first step in solving a system of equations involving fractions?

A: The first step in solving a system of equations involving fractions is to simplify the equations by eliminating the fractions. This can be done by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: How do I simplify the second equation in the system of equations?

A: To simplify the second equation, you can multiply both sides by the denominator of the fraction. This will eliminate the fraction and make it easier to solve for the variable.

Q: What is the difference between the two expressions for x in the system of equations?

A: The two expressions for x in the system of equations are x = 4y and 6x = ny. The first expression is obtained by simplifying the first equation, while the second expression is obtained by simplifying the second equation.

Q: How do I equate the two expressions for x in the system of equations?

A: To equate the two expressions for x, you can substitute one expression into the other. For example, you can substitute x = 4y into the equation 6x = ny to get 6(4y) = ny.

Q: What is the final step in solving for n in the system of equations?

A: The final step in solving for n is to simplify the equation and solve for n. In this case, we simplified the equation 6(4y) = ny to get 24y = ny, and then divided both sides by y to get n = 24.

Q: What are some common mistakes to avoid when solving for n in a system of equations?

A: Some common mistakes to avoid when solving for n in a system of equations include:

  • Not simplifying the equations before solving for n
  • Not equating the two expressions for x
  • Not simplifying the final equation before solving for n
  • Not checking the solution for n to make sure it is correct

Q: How can I practice solving for n in a system of equations?

A: You can practice solving for n in a system of equations by working through example problems and exercises. You can also try solving for n in different types of systems of equations, such as systems with multiple variables or systems with non-linear equations.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) about solving for n in a system of equations. We have covered topics such as simplifying the equations, equating the two expressions for x, and solving for n. By following these steps and avoiding common mistakes, you can solve for n in a system of equations with confidence.

Additional Resources

If you are looking for additional resources to help you solve for n in a system of equations, you may want to try the following:

  • Online tutorials and videos
  • Practice problems and exercises
  • Math textbooks and workbooks
  • Online communities and forums

Final Answer

The final answer is 24\boxed{24}.