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

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   • Two linear equations in the same two variables are said to form a pair of linear equations in two variables.
     • Can be represented or solved by graphical and algebraic method

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   • Two types of pair of equations consistent and inconsistent
     • 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 not equal to b1/b2 will have a unique point and one solution.
         • If a1/a2 is equal to b1/b2 is equal to c1/c2 will have coincident lines and infinitely many solutions
     • If the equation is inconsistent then it will have no 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 not equal to c1/c2 will have parallel lines and no solution

4. Methods for solving a pair of linear equations are ; Graphical method, Elimination method, Substitution method, Cross multiplication method, Matrix method and Determinants method