Solving the Equation 2y - 1 y - 3: A Comprehensive Guide for SEO
Solving algebraic equations is a fundamental skill in mathematics, and it is an essential concept in many fields such as engineering, physics, and economics. One common type of algebraic equation is the linear equation, which can be represented as ax b cx d. In this article, we will walk through the step-by-step process of solving the equation 2y - 1 y - 3.
Step-by-Step Solution of 2y - 1 y - 3
To solve the equation 2y - 1 y - 3, we need to isolate the variable y on one side of the equation and the constants on the other side.
Isolate the Variable
Start by moving all terms involving y to one side of the equation and all constant terms to the other side.
2y - 1 - y 3 - 1This simplifies to:
y - 1 3Now, to isolate y, we need to move the constant term -1 to the right side of the equation by adding 1 to both sides.
y - 1 1 3 1This simplifies to:
y 2Therefore, the solution to the equation 2y - 1 y - 3 is y 2.
Additional Examples and Variations
Let's explore a few more examples to reinforce the process of solving linear equations.
Example 1: 4y - 5 2y 3
To solve this equation, follow these steps:
4y - 5 - 2y 2y 3 - 2y 2y - 5 3 2y - 5 5 3 5 2y 8 2y / 2 8 / 2 y 4The solution to the equation 4y - 5 2y 3 is y 4.
Example 2: 3y - 2 5y 4
To solve this equation, follow these steps:
3y - 2 - 5y 5y 4 - 5y -2y - 2 4 -2y - 2 2 4 2 -2y 6 -2y / -2 6 / -2 y -3The solution to the equation 3y - 2 5y 4 is y -3.
Conclusion
Solving equations is a crucial skill in algebra. By following the steps outlined in this article, you can easily solve equations like 2y - 1 y - 3. The process involves isolating the variable on one side and moving all other terms to the other side of the equation. This technique is widely applicable in various math problems and is a fundamental concept for advanced studies in mathematics and related fields.