Solve The Formula A X + B Y = C A X + B Y = C A X + B Y = C For Y Y Y .A. Y = C − A X B Y = \frac{C - A X}{B} Y = B C − A X ​ B. Y = C + A X B Y = \frac{C + A X}{B} Y = B C + A X ​ C. Y = C − A X B Y = C - \frac{A X}{B} Y = C − B A X ​ D. Y = C B + A X Y = \frac{C}{B} + A X Y = B C ​ + A X

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 the formula $A x + B y = C$ for $y$. This equation is a classic example of a linear equation in two variables, and solving it requires a clear understanding of algebraic manipulation.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that 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 substitution, elimination, and graphing.

Solving the Formula $A x + B y = C$ for $y$

To solve the formula $A x + B y = C$ for $y$, we need to isolate the variable $y$ on one side of the equation. This can be done by subtracting $A x$ from both sides of the equation and then dividing both sides by $B$.

Step 1: Subtract $A x$ from Both Sides

The first step in solving the equation is to subtract $A x$ from both sides. This will give us:

$$B y = C - A x$$

Step 2: Divide Both Sides by $B$

Next, we need to divide both sides of the equation by $B$. This will give us:

$$y = \frac{C - A x}{B}$$

The Correct Solution

The correct solution to the equation $A x + B y = C$ for $y$ is:

$y = \frac{C - A x}{B}$

This solution can be verified by plugging it back into the original equation. If we substitute $y = \frac{C - A x}{B}$ into the original equation, we get:

$$A x + B \left(\frac{C - A x}{B}\right) = C$$

Simplifying this equation, we get:

$$A x + C - A x = C$$

Which is true for all values of $x$ and $C$.

Common Mistakes

When solving the equation $A x + B y = C$ for $y$, it is easy to make mistakes. Some common mistakes include:

• Adding $A x$ to both sides instead of subtracting it.
• Dividing both sides by $A$ instead of $B$.
• Not simplifying the equation properly.

Conclusion

Solving the formula $A x + B y = C$ for $y$ requires a clear understanding of algebraic manipulation and attention to detail. By following the steps outlined in this article, you can solve this equation with confidence. Remember to always verify your solution by plugging it back into the original equation.

Final Answer

The final answer to the equation $A x + B y = C$ for $y$ is:

$y = \frac{C - A x}{B}$

This solution is the correct answer, and it can be verified by plugging it back into the original equation.

Additional Resources

For more information on solving linear equations, check out the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

FAQs

Q: What is the formula for solving the equation $A x + B y = C$ for $y$? A: The formula for solving the equation $A x + B y = C$ for $y$ is $y = \frac{C - A x}{B}$.

Q: How do I verify my solution? A: To verify your solution, plug it back into the original equation and simplify it. If the equation is true for all values of $x$ and $C$, then your solution is correct.

$$$$ $$$$$$$$$$

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 provide a Q&A guide to help you understand how to solve linear equations, including the formula $A x + B y = C$ for $y$.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that 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 the equation $A x + B y = C$ for $y$?

A: To solve the equation $A x + B y = C$ for $y$, you need to isolate the variable $y$ on one side of the equation. This can be done by subtracting $A x$ from both sides of the equation and then dividing both sides by $B$.

Q: What is the formula for solving the equation $A x + B y = C$ for $y$?

A: The formula for solving the equation $A x + B y = C$ for $y$ is:

$y = \frac{C - A x}{B}$

Q: How do I verify my solution?

A: To verify your solution, plug it back into the original equation and simplify it. If the equation is true for all values of $x$ and $C$, then your solution is correct.

Q: What are some common mistakes to avoid when solving the equation $A x + B y = C$ for $y$?

A: Some common mistakes to avoid when solving the equation $A x + B y = C$ for $y$ include:

• Adding $A x$ to both sides instead of subtracting it.
• Dividing both sides by $A$ instead of $B$.
• Not simplifying the equation properly.

Q: Can I use other methods to solve the equation $A x + B y = C$ for $y$?

A: Yes, you can use other methods to solve the equation $A x + B y = C$ for $y$, such as substitution and elimination. However, the method outlined in this article is a simple and straightforward way to solve the equation.

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

A: Solving linear equations has many real-world applications, including:

• Physics: Solving linear equations is used to describe the motion of objects under the influence of forces.
• Engineering: Solving linear equations is used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Solving linear equations is used to model and analyze economic systems, including supply and demand.

Q: Can I use technology to solve linear equations?

A: Yes, you can use technology to solve linear equations, including calculators and computer software. However, it is still important to understand the underlying mathematics and be able to solve equations by hand.

Q: How do I practice solving linear equations?

A: To practice solving linear equations, try the following:

• Start with simple equations and gradually move on to more complex ones.
• Use online resources, such as Khan Academy and Mathway, to practice solving equations.
• Work with a partner or tutor to practice solving equations and get feedback on your work.

Conclusion

Solving linear equations is a fundamental skill that has many real-world applications. By understanding how to solve equations, including the formula $A x + B y = C$ for $y$, you can apply this skill to a wide range of problems. Remember to practice regularly and use technology to help you solve equations.