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Mathematics / Pair of Linear Equations in Two Variables

Mathematics / Pair of Linear Equations in Two Variables

A linear equation is an algebraic equation that contains terms which can either be constants or variables. The variables can only be of the first power.

A linear equation in two variables is of the form ax + by + c = 0, where x and y are variables and a, b and c are real numbers. Additionally a and b are non zero.

The graph of a linear equation in two variables plotted on a Cartesian plane is a straight line.

Given a pair of linear equations, they can be plotted as two lines in the Cartesian plane.

  • If the two lines intersect, the pair of equations is said to be consistent. Solving the two equations simultaneously yields a unique value for each of the two variables. These values represent the co-ordinates of the point of intersection.
  • If the two lines are parallel, the equations are inconsistent and there is no solution.
  • If the two lines are coincident, then there are infinite solutions since every point on these lines is a point of intersection and as we know the line extends infinitely.

Lessons
Topics
Lessons
Topics
    • Introduction to Pair of Linear equations in two variables
    • Pair of Linear Equations in Two Variables
    • Graphical Representation of a Pair of Linear Equations
    • Review of Pair of Linear equations in two variables
    • Determinant method of solving simultaneous equations
    • Condition of Consistency of Equations
    • Graphical Method of Solving Simultaneous Linear Equations
    • Algebraic Methods of Solving Simultaneous Linear Equations in Two Variables
    • Applications to Word Problems
  • Simultaneous Linear Equation in Two Variables

    Learnhive Lesson on Simultaneous Linear Equation in Two Variables

    • Accessed by: 120 Students

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