Solving Linear Equations: Addition and Subtraction Methods

Solving Linear Equations

Addition Method

• Used to solve systems of linear equations
• Steps:
  1. Write both equations in standard form (Ax + By = C)
  2. Add the equations to eliminate one variable
  3. Solve for the remaining variable
  4. 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:
  1. Write both equations in standard form (Ax + By = C)
  2. Subtract one equation from the other to eliminate one variable
  3. Solve for the remaining variable
  4. 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:
  1. Multiply both equations by necessary multiples to make the coefficients of one variable opposites
  2. Add or subtract the equations to eliminate one variable
  3. Solve for the remaining variable
  4. Substitute the value back into one of the original equations to find the other variable

Elimination Method

• Combines the Addition and Subtraction Methods
• Steps:
  1. Multiply both equations by necessary multiples to make the coefficients of one variable the same (or opposites)
  2. Add or subtract the equations to eliminate one variable
  3. Solve for the remaining variable
  4. 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