What Is The Value Of $x$ In The Equation $8x - 2y = 48$ When \$y = 4$[/tex\]?A. 6 B. 7 C. 14 D. 48

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Introduction to Solving Linear Equations

In mathematics, solving linear equations is a fundamental concept that involves finding the value of a variable in an equation. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving a linear equation with two variables, $x$ and $y$, and determine the value of $x$ when $y$ is given.

The Given Equation

The given equation is $8x - 2y = 48$. This is a linear equation with two variables, $x$ and $y$. The coefficients of $x$ and $y$ are 8 and -2, respectively. The constant term is 48.

Substituting the Value of $y$

We are given that $y = 4$. To find the value of $x$, we need to substitute this value into the equation. Substituting $y = 4$ into the equation, we get:

8x−2(4)=488x - 2(4) = 48

Simplifying the Equation

To simplify the equation, we need to evaluate the expression $-2(4)$. This is equal to $-8$. Therefore, the equation becomes:

8x−8=488x - 8 = 48

Isolating the Variable $x$

To isolate the variable $x$, we need to get rid of the constant term on the left-hand side of the equation. We can do this by adding 8 to both sides of the equation. This gives us:

8x=48+88x = 48 + 8

Evaluating the Expression

To evaluate the expression $48 + 8$, we need to add 48 and 8. This gives us:

8x=568x = 56

Dividing Both Sides by 8

To isolate the variable $x$, we need to divide both sides of the equation by 8. This gives us:

x=568x = \frac{56}{8}

Evaluating the Expression

To evaluate the expression $\frac{56}{8}$, we need to divide 56 by 8. This gives us:

x=7x = 7

Conclusion

In conclusion, the value of $x$ in the equation $8x - 2y = 48$ when $y = 4$ is 7.

Final Answer

The final answer is 7.

Frequently Asked Questions

Q: What is the value of $x$ in the equation $8x - 2y = 48$ when $y = 4$?

A: The value of $x$ in the equation $8x - 2y = 48$ when $y = 4$ is 7.

Q: How do I solve a linear equation with two variables?

A: To solve a linear equation with two variables, you need to isolate one of the variables by getting rid of the other variable. You can do this by adding or subtracting the same value to both sides of the equation.

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.

References

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Introduction

Solving linear equations is a fundamental concept in mathematics that involves finding the value of a variable in an equation. In this article, we will provide answers to frequently asked questions (FAQs) on 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 of ax + b = c, where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear equation with one variable?

A: To solve a linear equation with one variable, you need to isolate the variable by getting rid of the constant term. You can do this by adding or subtracting the same value to both sides of the equation.

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.

Q: How do I solve a linear equation with two variables?

A: To solve a linear equation with two variables, you need to isolate one of the variables by getting rid of the other variable. You can do this by adding or subtracting the same value to both sides of the equation.

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

A: The order of operations when solving a linear equation 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 check my answer when solving a linear equation?

A: To check your answer when solving a linear equation, you need to plug your solution back into the original equation and verify that it is true.

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
  • Not isolating the variable correctly
  • Not checking your answer
  • Not simplifying the equation

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms and eliminate any unnecessary variables or constants.

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

A: 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.

Q: How do I use linear equations to solve problems in real-world applications?

A: To use linear equations to solve problems in real-world applications, you need to:

  • Identify the variables and constants in the problem
  • Write a linear equation that models the problem
  • Solve the linear equation to find the solution
  • Check your answer to ensure that it is correct

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics that involves finding the value of a variable in an equation. By following the steps outlined in this article, you can solve linear equations with confidence and apply them to real-world problems.

Final Answer

The final answer is that solving linear equations is a crucial skill that can be applied to a wide range of real-world problems.

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