PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

1. General form of equations is: a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0, where a1,a2,b1,b2,c1,c2 are real numbers, such that a1square+b1square is not equal to 0, a2square+b2square is equal to 0

2. Two types of pair of equations consistent and inconsistent

   • If the equation is inconsistent then it will have no solutions.
     • conditions: let a pair of linear equation in two variables be a1x+b1y+c1=0 and a2x+b2y+c2=0. be,
       • If a1/a2 is equal to b1/b2 is not equal to c1/c2 will have parallel lines and no solution
   • If the equation is consistent then it will have either one or infinitely many solutions
     • Conditions: let a pair of linear equations in two variables be a1x+b1y+c1=0 and a2x+b2y+c2=0. be,
       • if a1/a2 is equal to b1/b2 is equal to c1/c2 will have coincident lines and infinitely many solutions.
       • If a1/a2 is not equal to b1/b2 will have a unique point and one solution

3. Methods for solving a pair of linear equations are : Graphical method, Elimination method , cross multiplication method, substitution method, Matrix method and Determinants method

4. The linear equations in the same two variables are said to form a pair of linear equations in two variables

   • Can be representated or solved by graphical or algebraic method