Solving for x in 3x7y 4y2x when y 2: A Comprehensive Guide

Understanding algebraic equations is crucial for a wide range of applications, from simple arithmetic problems to complex mathematical models. In this article, we will solve for x in the equation 3x7y 4y2x, given that y 2. This process involves algebraic manipulation and variable substitution.

Understanding the Problem

The given equation is 3x7y 4y2x. Our task is to find the value of x when y 2.

Simplifying the Equation

First, let's simplify the equation by subtracting the terms that involve x and y on both sides of the equation:

3x - 2x 4y - 7y

On simplifying further:

x -3y

Substituting the Value of y

Now that we have the simplified equation, let's substitute the value of y. Given y 2:

x -3(2)

Which simplifies to:

x -6

Conclusion and Verification

Therefore, the value of x is -6. To verify this, we can substitute x -6 and y 2 back into the original equation:

3x(-6)(2) 4(2)(-6)(2)

On simplifying:

-36 -96 / 4

-36 -36

This confirms that our solution is correct.

Frequently Asked Questions

Algebraic operations such as addition, subtraction, multiplication, and division are essential. These operations help in simplifying complex equations and finding unknown variables.

Yes, the same principle of variable substitution and algebraic manipulation can be applied to more complex equations, as long as the variables can be isolated and solved step by step.

The key guidelines are to simplify the equation by combining like terms, isolate the variable, and then substitute the known values to find the unknowns. It's also crucial to check your solution by substituting back into the original equation.

Related Keywords

Algebra, solving equations, variable substitution, mathematical solving, equation solving, algebraic problems, linear equations, basic algebra.