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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 the same variables, where solutions satisfy all equations simultaneously.
  • Substitution Method
    A process where one variable is isolated in an equation and its expression is inserted into another equation to simplify solving.
  • Variable
    A symbol, often x or y, representing an unknown value that can change within equations.
  • Expression
    A mathematical phrase combining numbers, variables, and operations, but lacking an equality sign.
  • Equation
    A mathematical statement asserting that two expressions are equal, often containing variables to solve for.
  • Solution
    A set of values for variables that make all equations in a system true when substituted.
  • Coefficient
    A numerical factor multiplied by a variable within an expression or equation.
  • Standard Form
    An arrangement of a linear equation where variables and constants are organized, typically as Ax + By = C.
  • Isolating a Variable
    The process of rearranging an equation so that one variable stands alone on one side of the equality.
  • True Statement
    An equation that holds valid after substituting specific values for its variables.
  • Parenthesis
    Curved symbols used to group parts of an expression, indicating operations to perform first.
  • Distribution
    A property used to multiply a single term across terms inside parenthesis, affecting each term within.
  • Guess and Check Method
    A trial approach where values are tested in equations to see if they satisfy all conditions.
  • Unknown
    A value represented by a variable that needs to be determined to solve an equation or system.
  • Step
    A distinct part of a procedure or method, such as isolating a variable or substituting values.