Identify The Equation Where The Value Of $y = 7$.A. $6y = 36$ B. $8y = 32$ C. $4y = 28$ D. $5y = 15$

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on identifying the equation where the value of y is equal to 7. We will analyze each option and determine which one satisfies the given condition.

Understanding Linear Equations

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable. In this case, we are dealing with equations in the form of ay = c, where a and c are constants, and y is the variable.

Analyzing the Options

Let's analyze each option and determine which one satisfies the condition y = 7.

Option A: $6y = 36$

To solve for y, we need to isolate y on one side of the equation. We can do this by dividing both sides of the equation by 6.

$$\frac{6y}{6} = \frac{36}{6}$$

This simplifies to:

$$y = 6$$

Since y is not equal to 7, this option is incorrect.

Option B: $8y = 32$

To solve for y, we need to isolate y on one side of the equation. We can do this by dividing both sides of the equation by 8.

$$\frac{8y}{8} = \frac{32}{8}$$

This simplifies to:

$$y = 4$$

Since y is not equal to 7, this option is incorrect.

Option C: $4y = 28$

To solve for y, we need to isolate y on one side of the equation. We can do this by dividing both sides of the equation by 4.

$$\frac{4y}{4} = \frac{28}{4}$$

This simplifies to:

$$y = 7$$

Since y is equal to 7, this option is correct.

Option D: $5y = 15$

To solve for y, we need to isolate y on one side of the equation. We can do this by dividing both sides of the equation by 5.

$$\frac{5y}{5} = \frac{15}{5}$$

This simplifies to:

$$y = 3$$

Since y is not equal to 7, this option is incorrect.

Conclusion

In conclusion, the correct equation where the value of y is equal to 7 is option C: $4y = 28$. This equation satisfies the condition y = 7, and solving for y yields the correct value.

Tips and Tricks

When solving linear equations, it's essential to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value. Additionally, make sure to simplify the equation by canceling out any common factors.

Practice Problems

Try solving the following linear equations:

1. $3x = 24$
2. $2y = 16$
3. $5x = 35$

Remember to isolate the variable on one side of the equation and simplify the equation by canceling out any common factors.

References

• Linear Equations
• Solving Linear Equations

About the Author

Introduction

In our previous article, we discussed how to identify the equation where the value of y is equal to 7. We analyzed each option and determined which one satisfies the given condition. In this article, we will provide a Q&A guide to help you better understand linear equations and how to solve them.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value. Make sure to simplify the equation by canceling out any common factors.

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

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation 2x + 3 = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I determine if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, look at the highest power of the variable(s). If the highest power is 1, the equation is linear. If the highest power is 2, the equation is quadratic.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Not isolating the variable on one side of the equation
• Not simplifying the equation by canceling out common factors
• Not checking the solution to make sure it satisfies the original equation

Q: How do I check if my solution is correct?

A: To check if your solution is correct, plug the solution back into the original equation and make sure it satisfies the equation. If the solution satisfies the equation, then it is correct.

Q: What are some real-world applications of linear equations?

A: Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future economic trends.

Q: How can I practice solving linear equations?

A: There are many ways to practice solving linear equations, including:

• Using online resources, such as Khan Academy and Mathway
• Working with a tutor or teacher
• Practicing with worksheets and exercises
• Solving real-world problems that involve linear equations

Conclusion

In conclusion, solving linear equations is an essential skill for students to master. By understanding the basics of linear equations and practicing with exercises and real-world problems, you can become proficient in solving linear equations and apply them to a variety of fields.

Tips and Tricks

• Make sure to isolate the variable on one side of the equation
• Simplify the equation by canceling out common factors
• Check the solution to make sure it satisfies the original equation
• Practice, practice, practice!

Practice Problems

Try solving the following linear equations:

1. $3x = 24$
2. $2y = 16$
3. $5x = 35$

Remember to isolate the variable on one side of the equation and simplify the equation by canceling out any common factors.

References

• Linear Equations
• Solving Linear Equations

About the Author

[Your Name] is a mathematics enthusiast with a passion for teaching and learning. With a strong background in mathematics, [Your Name] aims to provide high-quality content and resources for students and educators alike.