Pair of Linear Equation in Two Variables

Pair of Linear Equation in Two Variables

1. Standard Form of paired equations = a1x + b1y + c1 and a2x + b2y + c2

   • The linear equations are in the same two variables x and y. Equations like these are called a pair of linear equations in two variables.

2. Three cases of paired equation

   • case 1
     • When in the equation a1/a2 not= b1/b2
       • Unique solution exists
       • Two lines will be intersecting in the graph
       • Consistent set of equations
   • case 2
     • When a1/a2 = b1/b2 = c1/c2
       • Infinitely many solution exist
       • Two lines will coincident in the graph
       • Dependent consistent set of equations
   • case 3
     • When a1/a2 = b1/b2 not= c1/c2
       • Two lines will be parallel to each other
       • No solution exist
       • Inconsistent set of equation

3. Conclusion

4. Method of solving solutions

   • Elimination method
   • Cross multiplication method
   • Comparison method
   • Substitution method

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