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Solving Algebraic Equations: Finding the Value of Y when X 1
Solving Algebraic Equations: Finding the Value of Y when X 1
In this article, we will explore how to solve algebraic equations to find the value of a variable. Specifically, we will focus on the equation X 3Y - 2 and determine the value of Y when X 1. We will demonstrate step-by-step methods to solve this equation and explore the basic principles of algebraic manipulation.
Step-by-Step Guide to Solving the Equation
Given the equation:
X 3Y - 2
We are asked to find the value of Y when X 1. Let's proceed with the solution step-by-step:
Substitute X 1 into the equation:
1 3Y - 2
Add 2 to both sides of the equation to isolate the term containing Y:
1 2 3Y - 2 2
3 3Y
Divide both sides by 3 to solve for Y:
3/3 3Y/3
1 Y
Therefore, when X 1, the value of Y is 1.
This method involves basic algebraic operations such as addition and division, which are fundamental skills in solving algebraic equations.
Exploring Further: Solving Equations with Variables
Algebraic equations often involve variables that need to be solved for specific values. Understanding how to manipulate these equations is essential for solving a wide range of mathematical problems. Here are a few more examples to illustrate the process:
1. Example 1: If X 2Y 5, find the value of Y when X 11.
Given:
X 2Y 5
Substitute X 11 into the equation:
11 2Y 5
Subtract 5 from both sides:
11 - 5 2Y 5 - 5
6 2Y
Divide both sides by 2:
6/2 2Y/2
3 Y
Therefore, when X 11, the value of Y is 3.
2. Example 2: If X 4Y - 3, find the value of Y when X 5.
Given:
X 4Y - 3
Substitute X 5 into the equation:
5 4Y - 3
Add 3 to both sides:
5 3 4Y - 3 3
8 4Y
Divide both sides by 4:
8/4 4Y/4
2 Y
Therefore, when X 5, the value of Y is 2.
Conclusion
Solving algebraic equations is not only important in mathematics but also has practical applications in various fields such as engineering, physics, and economics. By mastering the basics of algebraic manipulation, you can tackle more complex problems with confidence.