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Solving Systems of Linear Equations by Elimination definitions

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  • Elimination Method
    A technique for solving systems by combining equations to remove a variable, streamlining the solution process.
  • System of Linear Equations
    A set of two or more equations with multiple variables, requiring simultaneous solutions for all variables.
  • Standard Form
    An arrangement where variables and constants are aligned vertically, typically as ax + by = c.
  • Coefficient
    A numerical factor attached to a variable, crucial for manipulating equations during elimination.
  • Variable
    A symbol representing an unknown quantity, targeted for elimination or isolation in solving systems.
  • Constant
    A fixed value in an equation, aligned with variables for vertical addition or subtraction.
  • Opposite Sign
    A pair of coefficients with equal magnitude but different signs, enabling cancellation during addition.
  • Multiplication
    An operation used to adjust coefficients, making them equal or opposite for effective elimination.
  • Addition
    A process of combining equations vertically, facilitating the removal of a variable.
  • Substitution Method
    An alternative approach where an isolated variable is replaced in another equation to simplify solving.
  • Isolated Variable
    A variable expressed alone on one side of an equation, ideal for substitution.
  • Trial and Error
    A strategy for testing different multipliers to achieve equal and opposite coefficients.
  • Factor
    A number that divides another coefficient evenly, guiding multiplication choices in elimination.
  • Vertical Alignment
    A setup where corresponding terms in equations are stacked, simplifying addition or subtraction.
  • Solution Pair
    A set of values for variables that satisfy all equations in a system, confirming correctness.