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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 whose solution satisfies all equations simultaneously.
  • Substitution Method
    A technique for solving systems by replacing a variable with its equivalent expression from another equation.
  • Variable
    A symbol, often x or y, representing an unknown value in an equation.
  • Expression
    A mathematical phrase combining numbers, variables, and operations without an equality sign.
  • Equation
    A mathematical statement asserting equality between two expressions.
  • Solution
    A set of values for variables that makes all equations in a system true.
  • Isolation
    The process of rearranging an equation to have a variable alone on one side.
  • Parenthesis
    Symbols used to group parts of an expression, affecting the order of operations.
  • Distribution
    Applying a multiplier to each term inside parentheses, often used when simplifying expressions.
  • Coefficient
    A numerical factor multiplying a variable in an algebraic expression.
  • True Statement
    An equation where substituted values result in both sides being equal.
  • Guess and Check
    A trial-and-error approach to finding solutions, less efficient than systematic methods.
  • Polynomial
    An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
  • Step
    A distinct part of a procedure or method, such as those in solving equations.
  • Unknown
    A value represented by a variable that needs to be determined in an equation.