Solving the Equations 5x - 25y 0 and 3x * 3y 9

Solving equations involves a series of steps to simplify expressions and isolate variables. In this article, we will walk through the process of solving the given equations:

Step 1: Simplify the First Equation

The first equation is 5x - 25y 0. We start by isolating one of the variables. Let's simplify and isolate x in terms of y.

Simplify the first equation:

5x 25y 0 x 25y 5 x 5y

After simplifying, we find that x 5y.

Step 2: Simplify the Second Equation

The second equation is 3x * 3y 9. We simplify this equation to find a relationship between x and y.

Simplify the second equation:

3x 3y 9 9xy 9 xy 1

From the simplified second equation, we can deduce that xy 1.

Step 3: Substitute and Solve for x and y

We now use the relationship between x and y to solve for individual values.

From the simplified first equation, we have x 5y. Substitute this into the second equation:

x 5 y

Substitute x 5y into xy 1 to get:

y 5y 1 y 2 1 5 y pm 1 5

Using these values of y, we can find the corresponding values of x using x 5y:

x 5 y x pm 5 5 pm 5

Thus, we have the solutions:

x pm 5 y pm 1 5

These solutions satisfy both original equations.

Conclusion

By simplifying and substituting, we found the solutions to the given equations. The process involved isolating variables, substituting, and solving quadratic equations. This method is a fundamental approach in algebra and can be applied to many other types of problems.

Related Reading

If you're interested in further improving your algebra skills, you might want to explore more about quadratic equations and systems of linear equations. Here are a few articles that can help you:

Understanding Quadratic Equations: A Comprehensive Guide

Solving Systems of Linear Equations with Examples

Algebraic Techniques for Solving Combinatorial Problems