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🔟elementary algebra review

key term - Multiplying Equations

Citation:

Definition

Multiplying equations is a technique used in solving systems of linear equations by elimination. It involves multiplying one or both equations in the system by a constant to create a new equation that, when combined with the original equations, results in the elimination of a variable, allowing for the solution of the system.

5 Must Know Facts For Your Next Test

  1. Multiplying equations is a key step in the elimination method for solving systems of linear equations.
  2. The goal of multiplying equations is to create a new equation that, when combined with the original equations, will eliminate one of the variables.
  3. Multiplying an equation by a constant does not change the solution to the equation, but it can make the coefficients more manageable for the elimination process.
  4. The choice of which equation to multiply and by what constant is crucial in ensuring successful elimination of a variable.
  5. Multiplying equations is often used in conjunction with other techniques, such as adding or subtracting equations, to solve more complex systems of linear equations.

Review Questions

  • Explain the purpose of multiplying equations in the context of solving systems of linear equations by elimination.
    • The purpose of multiplying equations in the context of solving systems of linear equations by elimination is to create a new equation that, when combined with the original equations, will eliminate one of the variables. By multiplying one or both equations in the system by a constant, the coefficients of the variables can be manipulated to allow for the successful elimination of a variable, ultimately leading to the solution of the system.
  • Describe the process of using the multiplying equations technique to solve a system of linear equations by elimination.
    • To use the multiplying equations technique to solve a system of linear equations by elimination, the following steps are typically followed: 1) Identify the variable to be eliminated. 2) Determine which equation(s) need to be multiplied and by what constant to create coefficients that will allow for the elimination of the selected variable. 3) Multiply the chosen equation(s) by the appropriate constant(s). 4) Combine the original and multiplied equations to eliminate the selected variable. 5) Solve the remaining equation(s) to find the values of the remaining variables.
  • Analyze the importance of selecting the appropriate equations and multiplication constants when using the multiplying equations technique to solve systems of linear equations.
    • The selection of the appropriate equations and multiplication constants is crucial when using the multiplying equations technique to solve systems of linear equations. The wrong choices can lead to an inability to eliminate a variable or create new equations that are more complex to work with. Careful consideration must be given to the coefficients of the variables in the original equations, as well as the desired outcome of the elimination process. The ability to strategically choose the equations and constants to manipulate is a key skill in successfully solving systems of linear equations using the elimination method.