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Solving Linear Equations definitions

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  • Linear Equation
    An algebraic statement in which the variable appears to the first power and can be written in the form ax+b=c.
  • Variable
    A symbol, often a letter, representing an unknown value that can be isolated to solve an equation.
  • Coefficient
    A numerical factor multiplying a variable, which can be a whole number, fraction, or decimal.
  • Constant
    A fixed value in an equation that does not change and is not attached to a variable.
  • Solution Set
    A collection of values that make an equation true when substituted for the variable.
  • Identity
    An equation true for all values of the variable, resulting in infinite solutions.
  • Contradiction
    An equation that is never true, leading to no solutions and an empty solution set.
  • Conditional Equation
    An equation true only for a specific value of the variable, yielding exactly one solution.
  • Property of Equality
    A rule allowing operations on both sides of an equation to maintain balance and equivalence.
  • Addition Property of Equality
    A principle stating that adding the same value to both sides of an equation preserves equality.
  • Subtraction Property of Equality
    A principle stating that subtracting the same value from both sides of an equation preserves equality.
  • Multiplication Property of Equality
    A principle stating that multiplying both sides of an equation by the same value preserves equality.
  • Division Property of Equality
    A principle stating that dividing both sides of an equation by the same nonzero value preserves equality.
  • Reciprocal
    A value that, when multiplied by a fraction, results in one, used to clear fractional coefficients.
  • Least Common Denominator
    The smallest shared multiple of denominators in an equation, used to clear fractions by multiplication.