Solve 7 X + 14 Y = 28 7x + 14y = 28 7 X + 14 Y = 28 For Y Y Y . □ \square □

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, $7x + 14y = 28$, for the variable $y$. We will break down the solution into manageable steps, making it easy to understand and follow.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $ax + by = c$, where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation $7x + 14y = 28$

The given equation is $7x + 14y = 28$. Our goal is to solve for $y$. To do this, we need to isolate $y$ on one side of the equation. We can start by subtracting $7x$ from both sides of the equation.

Subtracting $7x$ from Both Sides

7x + 14y = 28
7x - 7x + 14y = 28 - 7x
14y = 28 - 7x

Dividing Both Sides by 14

Now, we need to get rid of the coefficient of $y$, which is 14. We can do this by dividing both sides of the equation by 14.

14y = 28 - 7x
y = (28 - 7x) / 14

Simplifying the Expression

We can simplify the expression on the right-hand side of the equation by dividing both the numerator and the denominator by their greatest common divisor, which is 7.

y = (4 - x) / 2

Conclusion

In this article, we solved the linear equation $7x + 14y = 28$ for the variable $y$. We started by subtracting $7x$ from both sides of the equation, then divided both sides by 14 to isolate $y$. Finally, we simplified the expression on the right-hand side of the equation. The solution is $y = (4 - x) / 2$. This equation can be used to find the value of $y$ for any given value of $x$.

Example Use Case

Suppose we want to find the value of $y$ when $x = 2$. We can plug $x = 2$ into the equation $y = (4 - x) / 2$ to get:

y = (4 - 2) / 2
y = 2 / 2
y = 1

Therefore, when $x = 2$, the value of $y$ is 1.

Tips and Variations

• To solve a linear equation for a different variable, simply swap the variables in the equation.
• To solve a linear equation with multiple variables, use the method of substitution or elimination.
• To solve a linear equation with fractions, multiply both sides of the equation by the least common multiple of the denominators.

Common Mistakes to Avoid

• Don't forget to check your work by plugging the solution back into the original equation.
• Don't confuse the variables $x$ and $y$.
• Don't forget to simplify the expression on the right-hand side of the equation.

Conclusion

Introduction

In our previous article, we solved the linear equation $7x + 14y = 28$ for the variable $y$. We received many questions from readers who wanted to learn more about solving linear equations. In this article, we will answer some of the most frequently asked questions about solving linear equations.

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 $ax + by = c$, where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables.

Q: How do I solve a linear equation for a different variable?

A: To solve a linear equation for a different variable, simply swap the variables in the equation. For example, if we want to solve the equation $7x + 14y = 28$ for $x$, we can swap the variables to get $7y + 14x = 28$.

Q: How do I solve a linear equation with multiple variables?

A: To solve a linear equation with multiple variables, use the method of substitution or elimination. For example, if we have the equation $2x + 3y = 5$ and $x + 2y = 3$, we can use substitution to solve for $x$ and $y$.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, multiply both sides of the equation by the least common multiple of the denominators. For example, if we have the equation $\frac{2}{3}x + \frac{1}{2}y = 1$, we can multiply both sides by 6 to get $4x + 3y = 6$.

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 $x + 2y = 3$ is a linear equation, while the equation $x^2 + 2y = 3$ is a quadratic equation.

Q: How do I check my work when solving a linear equation?

A: To check your work when solving a linear equation, plug the solution back into the original equation. If the solution satisfies the equation, then it is correct.

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

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

• Forgetting to check your work
• Confusing the variables $x$ and $y$
• Forgetting to simplify the expression on the right-hand side of the equation
• Not following the order of operations

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 or Mathway
• Working with a tutor or teacher
• Practicing with worksheets or problems
• Solving real-world problems that involve linear equations

Conclusion

Solving linear equations is an essential skill in mathematics. By following the steps outlined in this article, you can solve linear equations for any variable. Remember to check your work, simplify the expression, and avoid common mistakes. With practice and patience, you will become proficient in solving linear equations and be able to tackle more complex equations with confidence.

Additional Resources

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations
• MIT OpenCourseWare: Linear Algebra

Final Tips

• Practice solving linear equations regularly to build your skills and confidence.
• Use online resources such as Khan Academy or Mathway to supplement your learning.
• Work with a tutor or teacher to get personalized feedback and guidance.
• Apply linear equations to real-world problems to see the relevance and importance of this skill.