What Is The Value Of $x$ In The Equation $8x - 2y = 48$, When $ Y = 4 Y = 4 Y = 4 [/tex]?A. 6 B. 7 C. 1 D. 14 E. 48
Introduction to Solving Linear Equations
Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to manipulate and solve equations to find the value of unknown variables. In this article, we will focus on solving a linear equation with two variables, $8x - 2y = 48$, where the value of $y$ is given as $4$. We will use algebraic methods to isolate the variable $x$ and find its value.
Understanding 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 $48$. We are given that the value of $y$ is $4$, and we need to find the value of $x$.
Substituting the Value of $y$
To find the value of $x$, we need to substitute the value of $y$ into the equation. We will replace $y$ with $4$ in the equation $8x - 2y = 48$. This gives us:
Simplifying the Equation
Now, we need to simplify the equation by evaluating the expression $-2(4)$. This gives us:
Isolating the Variable $x$
To isolate the variable $x$, we need to get rid of the constant term $-8$ on the left-hand side of the equation. We can do this by adding $8$ to both sides of the equation. This gives us:
Evaluating the Expression
Now, we need to evaluate the expression $48 + 8$. This gives us:
Dividing Both Sides by $8$
To find the value of $x$, we need to divide both sides of the equation by $8$. This gives us:
Evaluating the Expression
Now, we need to evaluate the expression $\frac{56}{8}$. This gives us:
Conclusion
In this article, we solved a linear equation with two variables, $8x - 2y = 48$, where the value of $y$ is given as $4$. We used algebraic methods to isolate the variable $x$ and find its value. The final answer is $x = 7$.
Frequently Asked Questions
- What is the value of $x$ in the equation $8x - 2y = 48$, when $y = 4$?
- How do you solve a linear equation with two variables?
- What is the final answer to the equation $8x - 2y = 48$, when $y = 4$?
Final Answer
The final answer is $x = 7$.
Introduction
Solving linear equations with two variables is a fundamental concept in mathematics. In our previous article, we solved a linear equation with two variables, $8x - 2y = 48$, where the value of $y$ is given as $4$. In this article, we will answer some frequently asked questions related to solving linear equations with two variables.
Q&A
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 $x = 7$.
Q: How do you 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 using algebraic methods. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by a constant.
Q: What is the final answer to the equation $8x - 2y = 48$, when $y = 4$?
A: The final answer to the equation $8x - 2y = 48$, when $y = 4$, is $x = 7$.
Q: How do you handle equations with negative coefficients?
A: When handling equations with negative coefficients, you need to remember that the negative sign can be moved to the other side of the equation by changing the sign of the term. For example, if you have the equation $-2x = 4$, you can move the negative sign to the other side by changing the sign of the term, giving you $2x = -4$.
Q: Can you give an example of a linear equation with two variables?
A: Yes, here is an example of a linear equation with two variables:
In this equation, $x$ and $y$ are the variables, and $3$ and $2$ are the coefficients.
Q: How do you solve a linear equation with two variables when the value of one variable is given?
A: To solve a linear equation with two variables when the value of one variable is given, you need to substitute the value of the given variable into the equation and then solve for the other variable. For example, if you have the equation $8x - 2y = 48$ and the value of $y$ is given as $4$, you can substitute $4$ for $y$ in the equation and then solve for $x$.
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 is $1$, while a quadratic equation is an equation in which the highest power of the variable is $2$. For example, the equation $3x + 2y = 12$ is a linear equation, while the equation $x^2 + 2y = 12$ is a quadratic equation.
Conclusion
In this article, we answered some frequently asked questions related to solving linear equations with two variables. We provided examples and explanations to help you understand how to solve linear equations with two variables. We hope this article has been helpful in clarifying any doubts you may have had.
Frequently Asked Questions
- What is the value of $x$ in the equation $8x - 2y = 48$, when $y = 4$?
- How do you solve a linear equation with two variables?
- What is the final answer to the equation $8x - 2y = 48$, when $y = 4$?
- How do you handle equations with negative coefficients?
- Can you give an example of a linear equation with two variables?
- How do you solve a linear equation with two variables when the value of one variable is given?
- What is the difference between a linear equation and a quadratic equation?
Final Answer
The final answer is $x = 7$.