Solving Systems Using Elimination: A Mathematical Approach, Study notes of Linear Algebra

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6.3 Solving Systems using Elimination objective: to solve systems by adding or subtracting to eliminate a variable

elimination method: uses the properties of adding and subtracting equations to eliminate a variable in the system Elimination involves algebraic manipulations of two or more equations. The end goal is to eliminate a variable by creating opposite coefficients.

Steps to Elimination

1. Multiply one or both equations so that one of the variables has the same coefficients with opposite signs.
2. Add the equations vertically so that one variable is eliminated.
3. Solve for the leftover variable.
4. Substitute the variable back into one of the original equations and solve for the opposite variable.

What is the solution to the systems?

• 3x3y=
  • 3x4y=
    • 5x6y=
    • 3x+6y=