Solve For \[$ Y \$\]:$\[ 8y - 9 = 31 \\]

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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 solving a linear equation of the form 8y - 9 = 31. We will break down the solution step by step, using clear and concise language to ensure that readers understand the process.

What is a Linear Equation?

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

The Equation to Solve

The equation we will be solving is 8y - 9 = 31. This equation is a linear equation, and we will use the steps outlined below to solve for y.

Step 1: Add 9 to Both Sides of the Equation

To solve for y, we need to isolate the variable on one side of the equation. The first step is to add 9 to both sides of the equation, which will eliminate the negative term.

8y - 9 + 9 = 31 + 9

This simplifies to:

8y = 40

Step 2: Divide Both Sides of the Equation by 8

Now that we have isolated the term with the variable, we can divide both sides of the equation by 8 to solve for y.

8y / 8 = 40 / 8

This simplifies to:

y = 5

Conclusion

In this article, we solved a linear equation of the form 8y - 9 = 31 using a step-by-step approach. We added 9 to both sides of the equation to eliminate the negative term, and then divided both sides of the equation by 8 to solve for y. The final solution is y = 5.

Tips and Tricks

  • When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you are performing the correct operations in the correct order.
  • When adding or subtracting terms, make sure to add or subtract the same value to both sides of the equation.
  • When multiplying or dividing terms, make sure to multiply or divide the same value to both sides of the equation.

Common Mistakes to Avoid

  • Not following the order of operations (PEMDAS) when solving linear equations.
  • Not adding or subtracting the same value to both sides of the equation.
  • Not multiplying or dividing the same value to both sides of the equation.

Real-World Applications

Linear equations have numerous 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.

Conclusion

Introduction

In our previous article, we covered the basics of solving linear equations. However, we know that practice makes perfect, and there's no better way to learn than by asking questions and getting answers. In this article, we'll provide a Q&A guide to help you better understand how to solve linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, y) is 1. Linear equations 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. You can do this by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides of the equation by the same value.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I add or subtract the same value to both sides of the equation?

A: To add or subtract the same value to both sides of the equation, you need to perform the operation on both sides of the equation. For example, if you have the equation 2x + 3 = 5, you can subtract 3 from both sides of the equation to get 2x = 2.

Q: How do I multiply or divide both sides of the equation by the same value?

A: To multiply or divide both sides of the equation by the same value, you need to perform the operation on both sides of the equation. For example, if you have the equation x/2 = 3, you can multiply both sides of the equation by 2 to get x = 6.

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

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

  • Not following the order of operations (PEMDAS)
  • Not adding or subtracting the same value to both sides of the equation
  • Not multiplying or dividing the same value to both sides of the equation
  • Not isolating the variable on one side of the equation

Q: How do I check my answer?

A: To check your answer, you can plug the value of the variable back into the original equation and see if it's true. For example, if you solved the equation 2x + 3 = 5 and got x = 1, you can plug x = 1 back into the original equation to get 2(1) + 3 = 5, which is true.

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

A: Linear equations have numerous 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.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving linear equations and apply your skills to real-world problems. Remember to follow the order of operations (PEMDAS), add or subtract the same value to both sides of the equation, and multiply or divide the same value to both sides of the equation. With practice and patience, you can become a master of solving linear equations.