Solve The Equation. Enter The Answer As An Equation That Shows The Value Of The Variable; For Example, $f=7$, Or $6=w$.$y-34=8$Answer Here:

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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 linear equations of the form y−34=8y - 34 = 8. We will break down the solution process into simple steps, making it easy for readers to understand and apply.

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+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable. Linear equations can be solved using various methods, including addition, subtraction, multiplication, and division.

Solving the Equation y−34=8y - 34 = 8

To solve the equation y−34=8y - 34 = 8, we need to isolate the variable yy. We can do this by adding 34 to both sides of the equation.

Step 1: Add 34 to Both Sides

When we add 34 to both sides of the equation, we are essentially "moving" the 34 from the left side of the equation to the right side. This leaves us with the variable yy on the left side, and the constant 42 on the right side.

y - 34 + 34 = 8 + 34

Step 2: Simplify the Equation

After adding 34 to both sides, we can simplify the equation by combining like terms. In this case, the 34 on the left side cancels out, leaving us with just the variable yy.

y = 42

Conclusion

In this article, we solved the linear equation y−34=8y - 34 = 8 using simple addition. We added 34 to both sides of the equation, which allowed us to isolate the variable yy. The final solution is y=42y = 42. This equation shows the value of the variable yy, which is 42.

Tips and Tricks

  • When solving linear equations, always follow the order of operations (PEMDAS).
  • Use addition and subtraction to isolate the variable.
  • Simplify the equation by combining like terms.
  • Check your solution by plugging it back into the original equation.

Real-World Applications

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 trends.

Common Mistakes

  • Forgetting to add or subtract the same value to both sides of the equation.
  • Not simplifying the equation by combining like terms.
  • Not checking the solution by plugging it back into the original equation.

Final Thoughts

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, readers can solve linear equations with ease. Remember to always follow the order of operations, use addition and subtraction to isolate the variable, simplify the equation by combining like terms, and check your solution by plugging it back into the original equation. With practice and patience, readers can become proficient in solving linear equations and apply them to real-world problems.

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Introduction

In our previous article, we covered the basics of solving linear equations. However, we know that practice makes perfect, and sometimes, it's helpful to have a Q&A guide to clarify any doubts. In this article, we will answer some 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. In other words, it is an equation that can be written in the form ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The order of operations is:

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

Q: How do I simplify an equation?

A: To simplify an equation, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, 2x2x and 3x3x are like terms, but 2x2x and 3y3y are not.

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. A quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, x+2=3x + 2 = 3 is a linear equation, but x2+2x+1=0x^2 + 2x + 1 = 0 is a quadratic equation.

Q: How do I check my solution?

A: To check your solution, you need to plug it back into the original equation and see if it is true. If it is true, then your solution is correct. If it is not true, then you need to go back and try again.

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 add or subtract the same value to both sides of the equation.
  • Not simplifying the equation by combining like terms.
  • Not checking the solution by plugging it back into the original equation.

Q: How do I apply linear equations to real-world problems?

A: Linear equations can be applied to a wide range of real-world problems, 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 trends.

Q: What are some tips for solving linear equations?

A: Some tips for solving linear equations include:

  • Always follow the order of operations.
  • Use addition and subtraction to isolate the variable.
  • Simplify the equation by combining like terms.
  • Check your solution by plugging it back into the original equation.

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, readers can solve linear equations with ease. Remember to always follow the order of operations, use addition and subtraction to isolate the variable, simplify the equation by combining like terms, and check your solution by plugging it back into the original equation. With practice and patience, readers can become proficient in solving linear equations and apply them to real-world problems.