This Will Be Your Opportunity To Be The Teacher Click On Vie

This Will Be Your Opportunity To Be The Teacher Click On View Full D

This will be your opportunity to be the teacher. Read the attached files: first, "MATH110 Read this first" to understand the instructions, then "Systems of Equations Problems with Answers." Pick one unsolved problem and demonstrate its solution using either the substitution or elimination method. Do not include the answer provided at the end of the file unless your solution matches it. In your post, include the problem statement, define your variables, write two equations based on the problem, state the method you are using, solve the system, and answer the question in a complete sentence. Do not respond to classmates' posts.

Paper For Above instruction

In many real-world scenarios, problems involving systems of equations are essential for modeling and solving complex situations. These systems often represent relationships involving multiple variables that interact with each other concurrently. The goal is to find the values of these variables that satisfy all the given equations simultaneously. Techniques such as substitution and elimination are fundamental tools in solving these systems efficiently and accurately.

Consider a typical problem scenario involving animals and people at a park, which can easily be translated into a system of equations. For example: "At a dog park, there are a total of 18 dogs and people combined, and there are 50 legs on all the animals and people." The problem asks for the number of dogs and people present at the park. To solve such a problem, we first define variables: let d represent the number of dogs and p represent the number of people.

Formulating the System of Equations

Based on the problem, molecules of equations emerge. For the total count of dogs and people, the equation is:

d + p = 18

since the total number of animals and people adds up to 18. Next, considering the total number of legs, dogs have 4 legs each, and people have 2 legs each, forming the second equation:

4d + 2p = 50

This system of equations now needs to be solved using an appropriate method. Here, I will choose the substitution method because one of the equations can be easily manipulated to isolate one variable.

Applying the Substitution Method

From the first equation, express p in terms of d:

p = 18 – d

Substitute this expression into the second equation:

4d + 2(18 – d) = 50

Distribute the 2 on the left side:

4d + 36 – 2d = 50

Combine like terms:

2d + 36 = 50

Subtract 36 from both sides:

2d = 14

Divide both sides by 2 to solve for d:

d = 7

Substitute d = 7 back into the expression for p:

p = 18 – 7 = 11

Therefore, there are 7 dogs and 11 people at the park.

Verification of the Solution

Verify the solution by checking the total legs:

4(7) + 2(11) = 28 + 22 = 50

The total matches the original problem statement, confirming that the solution is correct.

Discussion and Reflection

The process of solving the system using substitution was straightforward and efficient given the structure of the equations. This approach is particularly effective when one of the equations is already solved for one variable, simplifying the substitution process. In real-world applications like this, understanding how to set up and solve such systems is crucial for accurately modeling problems involving multiple interacting entities.

Alternative methods such as elimination could also be used, especially when the coefficients are aligned favorably for addition or subtraction. Both methods serve as valuable tools in an algebraic toolkit for solving complex systems encountered in various disciplines, including science, engineering, and business.

Conclusion

By defining variables, formulating equations, choosing an appropriate solving method, and verifying the solution, problems involving systems of equations can be tackled systematically. This example demonstrates how algebraic techniques can be applied effectively to real-world scenarios, exemplifying the importance of mastering these methods for academic and professional success.

References

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