Solve For { Y $} . . . { -59 = -7y + 4 \}

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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 specific type of linear equation, which is in the form of ax + b = c, where a, b, and c are constants. We will use the given equation -59 = -7y + 4 as an example to demonstrate the step-by-step process of solving for y.

Understanding the Equation

Before we dive into solving the equation, let's take a closer look at the given equation:

-59 = -7y + 4

In this equation, we have a constant term (-59) on the left-hand side, and a variable term (-7y) on the right-hand side. The constant term is the result of the equation, and the variable term is the unknown value that we need to solve for.

Step 1: Isolate the Variable Term

To solve for y, we need to isolate the variable term (-7y) on one side of the equation. We can do this by subtracting 4 from both sides of the equation:

-59 - 4 = -7y + 4 - 4

This simplifies to:

-63 = -7y

Step 2: Get Rid of the Negative Sign

The next step is to get rid of the negative sign in front of the variable term. We can do this by multiplying both sides of the equation by -1:

-63 × (-1) = -7y × (-1)

This simplifies to:

63 = 7y

Step 3: Solve for y

Now that we have isolated the variable term and gotten rid of the negative sign, we can solve for y by dividing both sides of the equation by 7:

63 ÷ 7 = 7y ÷ 7

This simplifies to:

9 = y

Conclusion

In this article, we have demonstrated the step-by-step process of solving a linear equation. We started with the given equation -59 = -7y + 4 and used algebraic manipulations to isolate the variable term and solve for y. The final answer is y = 9.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

  • Use inverse operations: To isolate the variable term, use inverse operations such as addition, subtraction, multiplication, and division.
  • Get rid of negative signs: To get rid of negative signs, multiply both sides of the equation by -1.
  • Check your work: Always check your work by plugging the solution back into the original equation.

Common Mistakes

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

  • Not isolating the variable term: Make sure to isolate the variable term on one side of the equation.
  • Not getting rid of negative signs: Make sure to get rid of negative signs by multiplying both sides of the equation by -1.
  • Not checking your work: Always check your work by plugging the solution 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 economic trends.

Conclusion

Introduction

In our previous article, we discussed the step-by-step process of solving linear equations. 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 is 1. It is typically written in the form of ax + b = c, where a, b, and c are constants.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the highest power of the variable. If the highest power is 1, then the equation is linear.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation has a highest power of 1, while a quadratic equation has a highest power of 2. For example, the equation 2x + 3 = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

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

A: To solve a linear equation with fractions, follow these steps:

  1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
  2. Simplify the equation by canceling out any common factors.
  3. Solve for the variable using inverse operations.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, make sure to check your work by plugging the solution back into the original equation.

Q: What is the order of operations when solving linear equations?

A: The order of operations when solving linear equations is:

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

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

A: Yes, you can solve a linear equation with multiple variables. However, you will need to use a system of linear equations to solve for all the variables.

Q: What is a system of linear equations?

A: A system of linear equations is a set of two or more linear equations that are solved simultaneously. For example:

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

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, follow these steps:

  1. Use the substitution method to substitute one equation into the other.
  2. Solve for the variable using inverse operations.
  3. Check your work by plugging the solution back into both original equations.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the step-by-step process outlined in this article, you can solve linear equations with ease. Remember to use inverse operations, get rid of negative signs, and check your work to ensure that you are solving the equation correctly. With practice and patience, you will become proficient in solving linear equations and be able to apply them to real-world problems.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

  • Use inverse operations: To isolate the variable term, use inverse operations such as addition, subtraction, multiplication, and division.
  • Get rid of negative signs: To get rid of negative signs, multiply both sides of the equation by -1.
  • Check your work: Always check your work by plugging the solution back into the original equation.
  • Use a calculator: You can use a calculator to solve linear equations, but make sure to check your work.
  • 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:

  • Not isolating the variable term: Make sure to isolate the variable term on one side of the equation.
  • Not getting rid of negative signs: Make sure to get rid of negative signs by multiplying both sides of the equation by -1.
  • Not checking your work: Always check your work by plugging the solution back into the original equation.
  • Not using inverse operations: Make sure to use inverse operations to isolate the variable term.
  • Not practicing enough: The more you practice solving linear equations, the more comfortable you will become with the process.