Solving Complex Equations: A Step-by-Step Guide for SEO and Content Writers

In the realm of algebra, solving equations can be a daunting task, but with the right approach, even complex equations can become manageable. This guide, designed for SEO professionals and content writers, provides a detailed breakdown of how to solve the given equations:

Understanding the Problem

The equations in question are:

x - frac{3}{2} 2y frac{1}{3} 3x - frac{1}{5} 12y frac{1}{2}

By breaking these equations down, we can solve for x and y, ultimately finding the values that satisfy both equations simultaneously.

Solving the First Equation

Starting with the first equation:

x - frac{3}{2} 2y frac{1}{3}

To solve for x and y, we need to manipulate the equation algebraically. The problem statement provides a detailed breakdown:

x - 2y frac{3}{2} frac{1}{3}

x - 2y frac{3 × 3}{2 × 3} frac{1 × 2}{3 × 2}

Therefore, x - 2y frac{11}{6}

This step involves simplifying the expression to isolate x and y.

Solving the Second Equation

Next, we tackle the second equation:

3x - frac{1}{5} 12y frac{1}{2}

This equation is similar to the first, but with different constants. We need to adjust the equation algebraically:

3x - 2y frac{3}{2} frac{1}{5}

3x - 2y frac{3 × 5}{2 × 5} frac{1 × 2}{5 × 2}

Therefore, 3x - 2y frac{17}{10}

This step again involves simplifying the expression to isolate x and y.

Combining the Equations

Now, we combine the two equations to solve for x and y.

3x - 2y - (x - 2y) frac{17}{10} - frac{11}{6}

30(2x) 30 left(frac{17}{10} - frac{11}{6} right)

6 51 - 55

x -frac{4}{60} - frac{1}{15}

3x - 2y - 3x - 2y frac{17}{10} - 3 left(frac{11}{6} right)

10(4y) 10 left(frac{17}{10} - frac{11}{2} right)

40y 17 - 55

y -frac{38}{40} -frac{19}{20}

Therefore, x - frac{1}{15} and y - frac{19}{20}

SEO Optimization Tips for Content Writers

For SEO professionals and content writers, it's important to optimize content that includes such detailed explanations. Here are some tips:

Keyword Integration: Use the primary keywords (equation solving, algebraic equations) throughout the content to make it search engine friendly. Headings: Utilize heading tags like H2 for subheadings to structure the content and make it easy to read. Image Optimization: Include images to illustrate the steps, making the content more engaging. Add alt text with the keywords to enhance SEO. Internal Linking: Link to related articles or guides within your website to create a cohesive content network.

By following these SEO best practices, you can ensure that your content is not only informative but also optimized for search engines.