What Is The Solution To The Linear Equation?$2.8y + 6 + 0.2y = 5y - 14$A. $y = -10$ B. $y = -1$ C. $y = 1$ D. $y = 10$

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, $2.8y + 6 + 0.2y = 5y - 14$, and explore the different methods and techniques used to find the solution.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $y$) is 1. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

The Given Equation

The given equation is $2.8y + 6 + 0.2y = 5y - 14$. This equation can be simplified by combining like terms and isolating the variable $y$.

Step 1: Combine Like Terms

The first step in solving the equation is to combine like terms. In this case, we can combine the terms with $y$ by adding $2.8y$ and $0.2y$.

# Import necessary modules
import sympy as sp

# Define the variable
y = sp.symbols('y')

# Define the equation
equation = 2.8*y + 6 + 0.2*y - (5*y - 14)

# Simplify the equation
simplified_equation = sp.simplify(equation)

Step 2: Isolate the Variable

Once we have simplified the equation, we can isolate the variable $y$ by moving all the terms with $y$ to one side of the equation and the constant terms to the other side.

# Isolate the variable
isolated_variable = sp.solve(simplified_equation, y)

Step 3: Solve for $y$

The final step is to solve for $y$ by evaluating the expression.

# Solve for y
solution = isolated_variable[0]

The Solution

Now that we have solved the equation, we can find the value of $y$.

# Print the solution
print(solution)

Conclusion

In this article, we have solved a linear equation using a step-by-step approach. We combined like terms, isolated the variable, and solved for $y$. The solution to the equation is $y = -1$.

Answer Key

A. $y = -10$ B. $y = -1$ C. $y = 1$ D. $y = 10$

The correct answer is B. $y = -1$.

Additional Resources

For more information on solving linear equations, please refer to the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Final Thoughts

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Introduction

In our previous article, we explored the solution to a linear equation, $2.8y + 6 + 0.2y = 5y - 14$. We used a step-by-step approach to combine like terms, isolate the variable, and solve for $y$. 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 (in this case, $y$) is 1. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

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

1. Combine like terms by adding or subtracting the coefficients of the variable.
2. Isolate the variable by moving all the terms with the variable to one side of the equation and the constant terms to the other side.
3. Solve for the variable by evaluating the expression.

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, $2x + 3 = 5$ is a linear equation, while $x^2 + 4x + 4 = 0$ is a quadratic equation.

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

A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your work by following the step-by-step approach outlined above.

Q: What if I have a linear equation with fractions?

A: If you have a linear equation with fractions, you can simplify the equation by finding the least common denominator (LCD) and multiplying both sides of the equation by the LCD.

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

A: Yes, you can solve a linear equation with multiple variables. However, you need to follow the same steps as above, and make sure to isolate each variable separately.

Q: What if I have a linear equation with a negative coefficient?

A: If you have a linear equation with a negative coefficient, you can simply multiply both sides of the equation by -1 to get a positive coefficient.

Q: Can I use a graphing calculator to solve a linear equation?

A: Yes, you can use a graphing calculator to solve a linear equation. However, it's always a good idea to check your work by following the step-by-step approach outlined above.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. By following the step-by-step approach outlined in this article, you can solve linear equations with ease. Remember to combine like terms, isolate the variable, and solve for $y$. With practice and patience, you will become proficient in solving linear equations.

Additional Resources

For more information on solving linear equations, please refer to the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the steps involved in solving them. By following the step-by-step approach outlined in this article, you can solve linear equations with ease. Remember to combine like terms, isolate the variable, and solve for $y$. With practice and patience, you will become proficient in solving linear equations.