What Is The Value Of $y$ In The Equation $5x + 2y = 20$, When \$x = 0.3$[/tex\]?A. 2.5 B. 28 C. 9.25 D. 10.75
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 $y$ when $x = 0.3$.
The Given Equation
The given equation is $5x + 2y = 20$. This equation represents a linear relationship between the variables $x$ and $y$. To find the value of $y$, we need to isolate $y$ on one side of the equation.
Isolating $y$
To isolate $y$, we need to get rid of the term $5x$ on the left-hand side of the equation. We can do this by subtracting $5x$ from both sides of the equation. This gives us:
Substituting the Value of $x$
Now that we have isolated $y$, we can substitute the value of $x$ into the equation. We are given that $x = 0.3$. Substituting this value into the equation, we get:
Evaluating the Expression
To evaluate the expression $20 - 5(0.3)$, we need to follow the order of operations (PEMDAS):
- Multiply $5$ and $0.3$: $5(0.3) = 1.5$
- Subtract $1.5$ from $20$: $20 - 1.5 = 18.5$
Simplifying the Equation
Now that we have evaluated the expression, we can simplify the equation:
Solving for $y$
To solve for $y$, we need to isolate $y$ on one side of the equation. We can do this by dividing both sides of the equation by $2$. This gives us:
Evaluating the Expression
To evaluate the expression $\frac{18.5}{2}$, we can divide $18.5$ by $2$:
Conclusion
In conclusion, the value of $y$ in the equation $5x + 2y = 20$, when $x = 0.3$, is $9.25$. This is the solution to the linear equation, and it represents the value of $y$ when $x$ is equal to $0.3$.
Discussion
The solution to the linear equation $5x + 2y = 20$, when $x = 0.3$, is $9.25$. This is a specific value of $y$ that satisfies the equation when $x$ is equal to $0.3$. The equation represents a linear relationship between the variables $x$ and $y$, and solving for $y$ involves isolating $y$ on one side of the equation.
Final Answer
The final answer is:
Introduction
In our previous article, we discussed how to solve a linear equation with two variables, $x$ and $y$. We used the equation $5x + 2y = 20$ and found the value of $y$ when $x = 0.3$. 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, and $x$ and $y$ are variables.
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 on one side of the equation. 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 (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an expression with fractions?
A: To evaluate an expression with fractions, you need to follow the order of operations (PEMDAS). If you have a fraction, you can multiply the numerator and denominator by the same value to eliminate the fraction.
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 $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $2x + 3y = 5$ is a linear equation.
Q: How do I solve a system of linear equations?
A: To solve a system of linear equations, you need to find the values of the variables that satisfy both equations. You can use substitution or elimination methods to solve a system of linear equations.
Q: What is the importance of solving linear equations?
A: Solving linear equations is an essential skill in mathematics and is used in many real-world applications, such as physics, engineering, economics, and computer science. It helps you to model and solve problems in a variety of fields.
Q: Can I use a calculator to solve linear equations?
A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to understand the steps involved in solving a linear equation and to check your answer using a calculator.
Q: How do I check my answer when solving a linear equation?
A: To check your answer when solving a linear equation, you can plug your solution back into the original equation and see if it's true. If it's true, then your solution is correct.
Conclusion
In conclusion, solving linear equations is an essential skill in mathematics that has many real-world applications. By understanding the concepts and techniques involved in solving linear equations, you can model and solve problems in a variety of fields. We hope that this Q&A article has helped you to better understand how to solve linear equations and has provided you with a solid foundation for further learning.
Final Answer
The final answer is: