The Value Of $m$ In The System Of Equations Is:${ \begin{array}{l} m - 2n = 8 \ n = M - 2 \end{array} }$A. -4 B. -6 C. 2 D. None Of These Choices Are Correct.

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Introduction

In mathematics, a system of equations is a set of equations that are all true at the same time. Solving a system of equations involves finding the values of the variables that make all the equations true. In this article, we will explore a system of two equations with two variables, mm and nn, and find the value of mm.

The System of Equations

The system of equations is given by:

{ \begin{array}{l} m - 2n = 8 \\ n = m - 2 \end{array} \}

Substitution Method

One way to solve this system of equations is by using the substitution method. This involves substituting the expression for one variable from one equation into the other equation. In this case, we can substitute the expression for nn from the second equation into the first equation.

Substituting nn into the First Equation

We can substitute n=m−2n = m - 2 into the first equation:

m−2(m−2)=8m - 2(m - 2) = 8

Simplifying the Equation

Now, we can simplify the equation by distributing the −2-2 and combining like terms:

m−2m+4=8m - 2m + 4 = 8

−m+4=8-m + 4 = 8

Solving for mm

Next, we can solve for mm by isolating it on one side of the equation. We can do this by subtracting 44 from both sides of the equation:

−m=8−4-m = 8 - 4

−m=4-m = 4

Multiplying Both Sides by −1-1

Finally, we can multiply both sides of the equation by −1-1 to solve for mm:

m=−4m = -4

Conclusion

In this article, we used the substitution method to solve a system of two equations with two variables, mm and nn. We found that the value of mm is −4-4. This is the correct answer, as it satisfies both equations in the system.

Discussion

The value of mm in a system of equations is an important concept in mathematics. It is used to solve systems of linear equations, which are a fundamental concept in algebra. The substitution method is one of the most common methods used to solve systems of equations, and it is a powerful tool for solving a wide range of mathematical problems.

Example Use Case

The value of mm in a system of equations has many practical applications in real-world problems. For example, in economics, the value of mm can be used to model the relationship between two variables, such as the price of a good and the quantity demanded. In physics, the value of mm can be used to model the motion of an object, such as the position and velocity of a particle.

Final Answer

The final answer is −4\boxed{-4}.

Related Topics

  • Solving Systems of Linear Equations
  • Substitution Method
  • Algebra
  • Mathematics

References

  • [1] "Solving Systems of Linear Equations" by Math Open Reference
  • [2] "Substitution Method" by Khan Academy
  • [3] "Algebra" by Wikipedia

Note: The references provided are for informational purposes only and are not intended to be a comprehensive list of resources on the topic.

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Introduction

In our previous article, we explored a system of two equations with two variables, mm and nn, and found the value of mm. In this article, we will answer some frequently asked questions (FAQs) about solving systems of equations.

Q&A

Q: What is a system of equations?

A: A system of equations is a set of equations that are all true at the same time. Solving a system of equations involves finding the values of the variables that make all the equations true.

Q: What are the different methods for solving systems of equations?

A: There are several methods for solving systems of equations, including:

  • Substitution Method: This involves substituting the expression for one variable from one equation into the other equation.
  • Elimination Method: This involves adding or subtracting the equations to eliminate one of the variables.
  • Graphical Method: This involves graphing the equations on a coordinate plane and finding the point of intersection.

Q: What is the substitution method?

A: The substitution method is a method for solving systems of equations that involves substituting the expression for one variable from one equation into the other equation.

Q: How do I use the substitution method?

A: To use the substitution method, follow these steps:

  1. Identify the equations and the variables.
  2. Choose one of the equations and solve it for one of the variables.
  3. Substitute the expression for the variable into the other equation.
  4. Simplify the equation and solve for the other variable.

Q: What is the elimination method?

A: The elimination method is a method for solving systems of equations that involves adding or subtracting the equations to eliminate one of the variables.

Q: How do I use the elimination method?

A: To use the elimination method, follow these steps:

  1. Identify the equations and the variables.
  2. Choose two of the equations and add or subtract them to eliminate one of the variables.
  3. Simplify the equation and solve for the other variable.

Q: What is the graphical method?

A: The graphical method is a method for solving systems of equations that involves graphing the equations on a coordinate plane and finding the point of intersection.

Q: How do I use the graphical method?

A: To use the graphical method, follow these steps:

  1. Graph the equations on a coordinate plane.
  2. Find the point of intersection of the two graphs.
  3. The point of intersection is the solution to the system of equations.

Conclusion

In this article, we answered some frequently asked questions (FAQs) about solving systems of equations. We discussed the different methods for solving systems of equations, including the substitution method, elimination method, and graphical method. We also provided step-by-step instructions for using each of these methods.

Discussion

Solving systems of equations is an important concept in mathematics. It is used to solve a wide range of mathematical problems, from simple linear equations to complex systems of nonlinear equations. The substitution method, elimination method, and graphical method are all powerful tools for solving systems of equations.

Example Use Case

The value of mm in a system of equations has many practical applications in real-world problems. For example, in economics, the value of mm can be used to model the relationship between two variables, such as the price of a good and the quantity demanded. In physics, the value of mm can be used to model the motion of an object, such as the position and velocity of a particle.

Final Answer

The final answer is −4\boxed{-4}.

Related Topics

  • Solving Systems of Linear Equations
  • Substitution Method
  • Elimination Method
  • Graphical Method
  • Algebra
  • Mathematics

References

  • [1] "Solving Systems of Linear Equations" by Math Open Reference
  • [2] "Substitution Method" by Khan Academy
  • [3] "Elimination Method" by Mathway
  • [4] "Graphical Method" by Wolfram Alpha

Note: The references provided are for informational purposes only and are not intended to be a comprehensive list of resources on the topic.