Luis Solves The Following System Of Equations By Elimination:$\[ \begin{cases} 5s + 3t = 30 \\ 2s + 3t = -3 \end{cases} \\]What Is The Value Of \[$ S \$\] In The Solution Of The System?A. \[$\frac{27}{7}\$\] B.
Introduction
Solving systems of equations is a fundamental concept in algebra, and one of the most effective methods for solving these systems is by elimination. In this article, we will explore how to solve a system of equations using the elimination method, with a focus on the problem presented by Luis. We will break down the solution step by step, providing a clear and concise explanation of each step.
The Problem
Luis is given a system of two linear equations with two variables, s and t. The system is as follows:
{ \begin{cases} 5s + 3t = 30 \\ 2s + 3t = -3 \end{cases} \}
The goal is to find the value of s in the solution of the system.
Step 1: Write Down the Equations
The first step in solving the system is to write down the two equations:
{ \begin{cases} 5s + 3t = 30 \\ 2s + 3t = -3 \end{cases} \}
Step 2: Multiply the Equations by Necessary Multiples
To eliminate one of the variables, we need to multiply the equations by necessary multiples such that the coefficients of t's in both equations are the same. We can multiply the first equation by 1 and the second equation by 1.
Step 3: Subtract the Second Equation from the First Equation
Now that we have the same coefficients for t in both equations, we can subtract the second equation from the first equation to eliminate the variable t.
{ (5s + 3t) - (2s + 3t) = 30 - (-3) \}
Simplifying the equation, we get:
{ 3s = 33 \}
Step 4: Solve for s
Now that we have eliminated the variable t, we can solve for s by dividing both sides of the equation by 3.
{ s = \frac{33}{3} \}
Simplifying the equation, we get:
{ s = 11 \}
Conclusion
In this article, we have solved a system of equations using the elimination method. We have broken down the solution step by step, providing a clear and concise explanation of each step. The final answer is that the value of s in the solution of the system is 11.
What is the Value of s?
The value of s in the solution of the system is 11.
Comparison with the Options
Let's compare our answer with the options provided:
A.
B. 11
Our answer matches option B.
Discussion
The elimination method is a powerful tool for solving systems of equations. By multiplying the equations by necessary multiples and subtracting one equation from the other, we can eliminate one of the variables and solve for the other. In this article, we have demonstrated how to solve a system of equations using the elimination method, with a focus on the problem presented by Luis. We hope that this article has provided a clear and concise explanation of the solution and has helped readers to understand the concept of solving systems of equations using the elimination method.
Final Answer
Introduction
In our previous article, we explored how to solve a system of equations using the elimination method. We broke down the solution step by step, providing a clear and concise explanation of each step. In this article, we will continue to provide more information on solving systems of equations using the elimination method, with a focus on answering frequently asked questions.
Q&A
Q: What is the elimination method?
A: The elimination method is a technique used to solve systems of equations by eliminating one of the variables. This is done by multiplying the equations by necessary multiples and subtracting one equation from the other.
Q: How do I know which variable to eliminate?
A: To determine which variable to eliminate, you need to look at the coefficients of the variables in both equations. If the coefficients of one variable are the same, you can eliminate that variable. If the coefficients are not the same, you need to multiply the equations by necessary multiples to make the coefficients the same.
Q: What if the coefficients of the variables are not the same?
A: If the coefficients of the variables are not the same, you need to multiply the equations by necessary multiples to make the coefficients the same. This will allow you to eliminate one of the variables.
Q: How do I multiply the equations by necessary multiples?
A: To multiply the equations by necessary multiples, you need to multiply both sides of the equation by the same number. For example, if you want to multiply the first equation by 2, you would multiply both sides of the equation by 2.
Q: What if I get a negative number when I multiply the equations?
A: If you get a negative number when you multiply the equations, you can simply change the sign of the number. For example, if you multiply the first equation by -2, you would change the sign of the number to make it positive.
Q: How do I subtract one equation from the other?
A: To subtract one equation from the other, you need to subtract the corresponding terms. For example, if you have the equation 2x + 3y = 5 and you want to subtract the equation x + 2y = 3, you would subtract the corresponding terms to get 2x - x + 3y - 2y = 5 - 3.
Q: What if I get a fraction when I subtract the equations?
A: If you get a fraction when you subtract the equations, you can simply simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
Q: Can I use the elimination method to solve systems of equations with more than two variables?
A: Yes, you can use the elimination method to solve systems of equations with more than two variables. However, you need to be careful when eliminating variables to make sure that you are not eliminating a variable that is not present in the system.
Q: What are some common mistakes to avoid when using the elimination method?
A: Some common mistakes to avoid when using the elimination method include:
- Not multiplying the equations by necessary multiples
- Not subtracting the corresponding terms
- Not simplifying the fraction
- Eliminating a variable that is not present in the system
Conclusion
In this article, we have provided a Q&A guide on solving systems of equations using the elimination method. We have answered frequently asked questions and provided tips and tricks to help you avoid common mistakes. We hope that this article has provided a clear and concise explanation of the elimination method and has helped readers to understand how to solve systems of equations using this technique.
Final Answer
The final answer is that the elimination method is a powerful tool for solving systems of equations, and by following the steps outlined in this article, you can use this method to solve systems of equations with confidence.