Follow The Given Steps To Solve For $y$.Step 1: Move The $x$ Term To The Other Side By Performing The Opposite Operation On BOTH Sides.$\[ \begin{array}{l} -7x + Y = -17 \\ +7x \end{array} \\]

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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 ax + by = c, where a, b, and c are constants. We will follow a step-by-step approach to solve for y, and provide examples to illustrate each step.

Step 1: Move the x term to the other side

The first step in solving a linear equation is to isolate the variable y. To do this, we need to move the x term to the other side of the equation. We can do this by performing the opposite operation on both sides of the equation.

For example, let's consider the equation -7x + y = -17. To move the x term to the other side, we need to add 7x to both sides of the equation.

-7x + y = -17
+7x + 7x

By adding 7x to both sides, we get:

y = -17 + 7x

Discussion

In this step, we have successfully moved the x term to the other side of the equation. This is an important step in solving linear equations, as it allows us to isolate the variable y.

Step 2: Simplify the equation

Once we have moved the x term to the other side, we can simplify the equation by combining like terms.

For example, let's consider the equation y = -17 + 7x. We can simplify this equation by combining the constant terms.

y = -17 + 7x
y = -17 + 7x

By combining the constant terms, we get:

y = 7x - 17

Discussion

In this step, we have simplified the equation by combining like terms. This is an important step in solving linear equations, as it helps to make the equation easier to work with.

Step 3: Solve for y

Now that we have simplified the equation, we can solve for y. To do this, we need to isolate the variable y.

For example, let's consider the equation y = 7x - 17. We can solve for y by adding 17 to both sides of the equation.

y = 7x - 17
+17 + 17

By adding 17 to both sides, we get:

y = 7x

Discussion

In this step, we have successfully solved for y. This is the final step in solving a linear equation, and it allows us to find the value of y.

Conclusion

Solving linear equations is an important skill for students to master. By following the steps outlined in this article, we can solve linear equations of the form ax + by = c. We have seen how to move the x term to the other side, simplify the equation, and solve for y. With practice and patience, students can become proficient in solving linear equations and apply this skill to a wide range of mathematical problems.

Examples

Here are some examples of linear equations that we can solve using the steps outlined in this article:

  • 2x + 3y = 5
  • 4x - 2y = 3
  • x + 2y = 4

Tips and Tricks

Here are some tips and tricks for solving linear equations:

  • Make sure to perform the opposite operation on both sides of the equation.
  • Simplify the equation by combining like terms.
  • Solve for y by isolating the variable y.
  • Practice, practice, practice! The more you practice solving linear equations, the more comfortable you will become with the process.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

  • Failing to perform the opposite operation on both sides of the equation.
  • Failing to simplify the equation by combining like terms.
  • Failing to solve for y by isolating the variable y.
  • Making careless errors when performing calculations.

Conclusion

Introduction

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the steps involved in solving these equations. In our previous article, we provided a step-by-step guide on how to solve linear equations of the form ax + by = c. 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. It can be written in the form ax + by = c, where a, b, and c are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to follow these steps:

  1. Move the x term to the other side of the equation by performing the opposite operation on both sides.
  2. Simplify the equation by combining like terms.
  3. Solve for y by isolating the variable y.

Q: What is the opposite operation?

A: The opposite operation is the operation that "reverses" the given operation. For example, if the given operation is addition, the opposite operation is subtraction. If the given operation is multiplication, the opposite operation is division.

Q: How do I know which operation to perform?

A: To determine which operation to perform, you need to look at the coefficient of the x term. If the coefficient is positive, you need to perform the opposite operation on both sides. If the coefficient is negative, you need to perform the same operation on both sides.

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

Q: Can I solve a linear equation with multiple variables?

A: Yes, you can solve a linear equation with multiple variables. To do this, you need to follow the same steps as before, but you need to isolate each variable separately.

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

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

  • Failing to perform the opposite operation on both sides of the equation.
  • Failing to simplify the equation by combining like terms.
  • Failing to solve for y by isolating the variable y.
  • Making careless errors when performing calculations.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through examples and exercises. You can also use online resources, such as math websites and apps, to practice solving linear equations.

Conclusion

Solving linear equations is an essential skill for students to master. By following the steps outlined in this article, you can solve linear equations of the form ax + by = c. We have answered some frequently asked questions about solving linear equations, and provided tips and tricks for avoiding common mistakes. With practice and patience, you can become proficient in solving linear equations and apply this skill to a wide range of mathematical problems.

Additional Resources

Here are some additional resources for practicing solving linear equations:

  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • IXL: Linear Equations
  • MIT OpenCourseWare: Linear Algebra

Final Tips

Here are some final tips for solving linear equations:

  • Practice, practice, practice! The more you practice solving linear equations, the more comfortable you will become with the process.
  • Make sure to perform the opposite operation on both sides of the equation.
  • Simplify the equation by combining like terms.
  • Solve for y by isolating the variable y.
  • Avoid making careless errors when performing calculations.