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Solving Systems of Linear Equations by Substitution definitions

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  • System of Equations
    A set of two or more equations with shared variables, requiring a solution that satisfies all equations simultaneously.
  • Substitution Method
    A process where one equation is rearranged to isolate a variable, then its expression is inserted into another equation to solve.
  • Variable
    A symbol, often x or y, representing an unknown value to be determined within equations.
  • Expression
    A mathematical phrase combining numbers, variables, and operations, but lacking an equals sign.
  • Equation
    A mathematical statement showing equality between two expressions, often containing variables.
  • Solution
    A pair of values for variables that, when substituted, make all equations in a system true.
  • Coefficient
    A numerical factor multiplied by a variable within an equation or expression.
  • Standard Form
    An arrangement of an equation where variables and constants are organized, typically as Ax + By = C.
  • True Statement
    An equation that holds valid when specific values are substituted for its variables.
  • Parenthesis
    Symbols used to group parts of an expression, indicating operations should be performed first.
  • Distribution
    The process of multiplying a term across terms inside parentheses, affecting each part within.
  • Isolating a Variable
    Rearranging an equation so a single variable stands alone on one side, ready for substitution.
  • Plugging In
    Replacing a variable with a specific value or expression within an equation to simplify or solve.
  • Polynomial
    An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
  • Guess and Check
    A trial-and-error approach to finding solutions, often inefficient compared to systematic methods.