Solve: 3 X − 2 Y 3x - 2y 3 X − 2 Y When X = 2 X = 2 X = 2 And Y = 10 Y = 10 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 linear equation with two variables, $x$ and $y$, using a specific set of values. We will use the equation $3x - 2y$ and substitute the given values of $x = 2$ and $y = 10$ to find the solution.

What are Linear Equations?

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. Linear equations can be solved using various methods, including substitution, elimination, and graphing.

The Equation $3x - 2y$

The equation $3x - 2y$ is a linear equation with two variables, $x$ and $y$. To solve this equation, we need to substitute the given values of $x$ and $y$ into the equation.

Substituting Values

We are given the values of $x = 2$ and $y = 10$. We can substitute these values into the equation $3x - 2y$ as follows:

$$3(2) - 2(10)$$

Simplifying the Equation

To simplify the equation, we need to follow the order of operations (PEMDAS):

1. Multiply 3 and 2: $3(2) = 6$
2. Multiply 2 and 10: $2(10) = 20$
3. Subtract 20 from 6: $6 - 20 = -14$

The Final Answer

Therefore, the solution to the equation $3x - 2y$ when $x = 2$ and $y = 10$ is:

$$-14$$

Conclusion

Solving linear equations is an essential skill in mathematics, and it requires a clear understanding of the concept of linear equations and the methods used to solve them. In this article, we used the equation $3x - 2y$ and substituted the given values of $x = 2$ and $y = 10$ to find the solution. We simplified the equation using the order of operations and arrived at the final answer of $-14$.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects, including velocity, acceleration, and force.
• Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and control systems.
• Economics: Linear equations are used to model economic systems, including supply and demand, production costs, and profit maximization.

Tips and Tricks

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

• Use the order of operations: Follow the order of operations (PEMDAS) to simplify the equation.
• Substitute values carefully: Make sure to substitute the correct values into the equation.
• Check your work: Verify that your solution is correct by plugging it back into the original equation.

Common Mistakes

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

• Incorrect substitution: Make sure to substitute the correct values into the equation.
• Incorrect simplification: Follow the order of operations (PEMDAS) to simplify the equation.
• Incorrect solution: Verify that your solution is correct by plugging it back into the original equation.

Conclusion

$$$$$$$$

Introduction

In our previous article, we discussed how to solve linear equations using the equation $3x - 2y$ and substituting the given values of $x = 2$ and $y = 10$. In this article, we will provide a Q&A guide to help you understand and solve 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?

A: To solve a linear equation, you can use the following methods:

• Substitution method: Substitute the given values of the variables into the equation.
• Elimination method: Eliminate one of the variables by adding or subtracting the equations.
• Graphing method: Graph the equations on a coordinate plane and find the point of intersection.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an equation. The order of operations 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 simplify an equation?

A: To simplify an equation, follow the order of operations:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

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 system of linear equations?

A: To solve a system of linear equations, you can use the following methods:

• Substitution method: Substitute the given values of one variable into the other equation.
• Elimination method: Eliminate one of the variables by adding or subtracting the equations.
• Graphing method: Graph the equations on a coordinate plane and find the point of intersection.

Q: What is the significance of linear equations in real-world applications?

A: Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects, including velocity, acceleration, and force.
• Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and control systems.
• Economics: Linear equations are used to model economic systems, including supply and demand, production costs, and profit maximization.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Incorrect substitution: Make sure to substitute the correct values into the equation.
• Incorrect simplification: Follow the order of operations (PEMDAS) to simplify the equation.
• Incorrect solution: Verify that your solution is correct by plugging it back into the original equation.

Conclusion

Solving linear equations is a crucial skill in mathematics, and it requires a clear understanding of the concept of linear equations and the methods used to solve them. In this article, we provided a Q&A guide to help you understand and solve linear equations. We also discussed the significance of linear equations in real-world applications and provided tips and tricks to help you avoid common mistakes.