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Solving Systems of Linear Equations by Elimination definitions

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  • Elimination Method
    A technique for solving systems by adding equations to remove a variable, often after adjusting coefficients to be equal and opposite.
  • System of Linear Equations
    A set of two or more equations with the same variables, where solutions satisfy all equations simultaneously.
  • Standard Form
    An arrangement of equations as ax + by = c, aligning variables and constants vertically for easier manipulation.
  • Coefficient
    A numerical factor multiplying a variable, crucial for aligning and eliminating variables in equations.
  • Variable
    A symbol, often x or y, representing unknown values to be determined in equations.
  • Constant
    A fixed value in an equation, not multiplied by a variable, typically found on the right side of standard form.
  • Opposite Sign
    A pair of numbers with identical values but different signs, such as 3 and -3, used to cancel variables.
  • Multiples
    Numbers obtained by multiplying a value by integers, used to align coefficients for elimination.
  • Substitution Method
    A process where one variable is isolated and replaced in another equation to simplify solving.
  • Trial and Error
    A strategy involving testing different multipliers to achieve equal and opposite coefficients for elimination.
  • Isolated Variable
    A variable expressed alone on one side of an equation, making substitution straightforward.
  • True Statement
    An equation that holds valid when solution values are substituted, confirming correctness.
  • Vertical Alignment
    The arrangement of equations so that like terms are stacked, facilitating addition or subtraction.
  • Factor
    A number that divides another exactly, used to determine suitable multipliers for coefficients.
  • Solution Pair
    A set of values for variables that satisfy all equations in a system.