Pair of Linear Equations in Two Variables

Pair of Linear Equations in Two Variables

1. Linear Equations in Two Variables- ax + by + c = 0, where a, b and c are real numbers and a, b ≠ 0.

   • Form of a pair of linear equations in Two Variables- a1x + b1 y + c1 = 0, a2x + b2 y + c2 = 0
     • a1/a2 ≠ b1/b2
       • Consistent Equations
     • a1/a2 = b1/b2 ≠ c1/c2
       • Inconsistent Equations
     • a1/a2 = b1/b2 = c1/c2
       • Dependent Equations

2. Types of equations based on the number of solutions

   • One solution- Consistent Equations
   • No solution- Inconsistent Equations
   • Infinitely many solutions- Dependent Equations

3. Methods of solving equations

   • Algebraic method
     • Substitution Method
     • Elimination Method
     • Cross-multiplication Method
   • Graphical method

4. Graphical Representation of Linear Equations in Two Variables

   • The two lines formed by the equations will intersect at one point
     • Consistent Equations
   • The two lines formed by the equations will not intersect, i.e., they are parallel.
     • Inconsistent Equations
   • The two lines formed by the equations will be coincident.
     • Dependent Equations

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