9 Questions
What is the main purpose of the Addition Method in solving systems of linear equations?
To eliminate one variable
In what step of the Subtraction Method do you eliminate one variable?
Step 2: Subtract one equation from the other
What is a key characteristic of the Multiplication Method?
It is used when the coefficients of one variable are opposites
What is the main difference between the Addition Method and the Subtraction Method?
The method used to eliminate one variable
What is the purpose of multiplying both equations by necessary multiples in the Elimination Method?
To make the coefficients of one variable the same
In what step of the Elimination Method do you solve for the remaining variable?
Step 3: Solve for the remaining variable
What is the main advantage of using the Elimination Method over the other methods?
It combines the Addition and Subtraction Methods
In what method is it necessary to rewrite the equations in standard form?
All of the above
What is the final step in all the methods for solving systems of linear equations?
Substitute the value back into one of the original equations
Study Notes
Solving Linear Equations
Addition Method
- Used to solve systems of linear equations
- Steps:
- Write both equations in standard form (Ax + By = C)
- Add the equations to eliminate one variable
- Solve for the remaining variable
- Substitute the value back into one of the original equations to find the other variable
Subtraction Method
- Similar to the Addition Method, but subtracts one equation from the other
- Steps:
- Write both equations in standard form (Ax + By = C)
- Subtract one equation from the other to eliminate one variable
- Solve for the remaining variable
- Substitute the value back into one of the original equations to find the other variable
Multiplication Method
- Used when the coefficients of one variable are opposites (e.g., 2x and -2x)
- Steps:
- Multiply both equations by necessary multiples to make the coefficients of one variable opposites
- Add or subtract the equations to eliminate one variable
- Solve for the remaining variable
- Substitute the value back into one of the original equations to find the other variable
Elimination Method
- Combines the Addition and Subtraction Methods
- Steps:
- Multiply both equations by necessary multiples to make the coefficients of one variable the same (or opposites)
- Add or subtract the equations to eliminate one variable
- Solve for the remaining variable
- Substitute the value back into one of the original equations to find the other variable
Solving Linear Equations
Methods Overview
- There are four methods to solve systems of linear equations: Addition, Subtraction, Multiplication, and Elimination
Addition Method
- Used to solve systems of linear equations
- Eliminates one variable by adding the equations
- Four-step process: write equations in standard form, add equations, solve for one variable, and substitute to find the other variable
Subtraction Method
- Similar to Addition Method, but subtracts one equation from the other
- Also a four-step process: write equations in standard form, subtract equations, solve for one variable, and substitute to find the other variable
Multiplication Method
- Used when coefficients of one variable are opposites (e.g., 2x and -2x)
- Multiplies equations to make coefficients of one variable opposites, then adds or subtracts to eliminate one variable
- Four-step process: multiply equations, add or subtract, solve for one variable, and substitute to find the other variable
Elimination Method
- Combines Addition and Subtraction Methods
- Multiplies equations to make coefficients of one variable the same or opposites
- Four-step process: multiply equations, add or subtract, solve for one variable, and substitute to find the other variable
This quiz covers the methods of solving systems of linear equations, including the addition and subtraction methods. Learn the steps to eliminate variables and find solutions.
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