Solving Simultaneous Equations with Google SEO Optimization

In this article, we will demonstrate the process of solving simultaneous equations using algebraic methods. Specifically, we will solve the problem 3x 4y 20 and x - y 5 to find the values of x and y. By understanding the methods outlined below, you can optimize your Google SEO and find this solution more easily when searching for related algebraic problems.

Solving Simultaneous Equations: Step-by-Step Guide

Simultaneous equations involve solving a system of equations with the same variables. In this case, we have:

3x 4y 20 eqn 1

x - y 5 eqn 2

Step 1: Expressing One Variable from the Second Equation

Starting with the second equation, x - y 5,

we can express x in terms of y:

x 5 y

Step 2: Substituting the Expression into the First Equation

Substitute x 5 y into the first equation, 3x 4y 20:

3(5 y) 4y 20

Step 3: Solving for y

Simplify and solve for y:

15 3y 4y 20 7y 5 y frac{5}{7}

Step 4: Substituting y Back into the Expression for x

Now substitute y frac{5}{7} back into the expression x 5 y:

x 5 frac{5}{7} x frac{35}{7} frac{5}{7} x frac{40}{7}

Step 5: Verifying the Solution

Finally, we can check our solution by verifying that the values of x and y satisfy both original equations:

3x 4y 20 3 cdot frac{40}{7} 4 cdot frac{5}{7} 20 frac{120}{7} frac{20}{7} 20 frac{140}{7} 20

Both equations are satisfied, confirming our solution.

The Solution

Thus, the values are:

x frac{40}{7}, y frac{5}{7} x y frac{40}{7} frac{5}{7} frac{45}{7}

Our final answer is:

x y frac{45}{7}

Practical Application and SEO Optimization for Simultaneous Equations

Understanding how to solve simultaneous equations, such as the one presented, is crucial in fields like engineering, physics, and economics. For writers, educators, and students, optimizing for Google SEO requires including specific terms and methods that reflect the problem-solving process clearly. When writing about this topic, include relevant keywords like "simultaneous equations" and "algebra" to enhance the chances of being found in search results. Additionally, making use of detailed step-by-step guides and clear mathematical expressions helps in providing comprehensive content that is easily understandable and SEO-friendly.

For further reading, consider exploring related algebraic topics such as linear equations, systems of equations, and methods for solving such equations. These topics not only enhance your understanding but also provide more keywords and content to optimize for SEO purposes.