Solve For Y 2x Y 3

Solving for y: A Step-by-Step Guide to 2x + y = 3

This article provides a comprehensive guide on how to solve the simple algebraic equation, 2x + y = 3, for the variable 'y'. Understanding this process is fundamental to mastering algebra and lays the groundwork for solving more complex equations. We will break down the steps clearly and concisely, making it easy to understand even for beginners.

Understanding the Goal:

Our objective is to isolate 'y' on one side of the equation. This means manipulating the equation using algebraic rules until we have 'y = [expression]'. The expression on the right-hand side will involve 'x' and constants.

Step-by-Step Solution:

1. Identify the Term with 'y': In the equation 2x + y = 3, the term containing 'y' is simply 'y'.

2. Isolate the 'y' Term: To isolate 'y', we need to move the '2x' term to the right-hand side of the equation. We achieve this by subtracting '2x' from both sides of the equation. This maintains the equality of the equation.

   2x + y - 2x = 3 - 2x

3. Simplify: This simplifies to:

   y = 3 - 2x

Therefore, the solution for 'y' is y = 3 - 2x.

Understanding the Solution:

This equation, y = 3 - 2x, represents a linear relationship between 'x' and 'y'. For every value of 'x' you substitute into the equation, you will get a corresponding value for 'y'. This equation can be used to find points on a straight line graph. You can easily plot these points and visualize the relationship.

Practical Applications and Further Exploration:

This fundamental skill of solving for a variable is crucial in many areas, including:

• Mathematics: Solving more complex equations and inequalities.
• Science: Modeling physical phenomena and analyzing data.
• Computer Science: Developing algorithms and creating mathematical models.
• Economics: Analyzing economic relationships and making predictions.

This simple equation provides a solid foundation for tackling more advanced algebraic concepts. By practicing similar problems, you can build confidence and proficiency in solving algebraic equations. Try substituting different values for 'x' to see how the corresponding 'y' values change. This will help reinforce your understanding of the relationship between the variables. Furthermore, explore similar equations, perhaps involving multiplication or division, to further solidify your algebraic skills. Remember, practice is key to mastering this essential skill.