Linear Equations in Two Variables.

LINEAR EQUATIONS IN TWO VARIABLES : 2/6/2009 DK Arya 1 LINEAR EQUATIONS IN TWO VARIABLES General Form : ax+by+c=0 where, (1) a & b does not equal to zero. (2) a,b,&c are real nos. Its solution is a pair of values,one for x & other for y.

Ways To Solve Pair Of Linear Equations : 2/6/2009 DK Arya 2 Ways To Solve Pair Of Linear Equations Graphical Method Algebraic Method Cross Multiplication Method

GRAPHICAL METHOD : 2/6/2009 DK Arya 3 GRAPHICAL METHOD 1)The Eqs. have a Unique common solution if in the graph, the lines intersect in a single point. 2)The Eqs. have no common solution if lines are parallel. 3)The Eqs. have infinitely many solutions if lines are coincident.

ALGEBRAIC METHOD : 2/6/2009 DK Arya 4 ALGEBRAIC METHOD Elimination by SUBSTITUTION (Solving eq.1 for y and putting y’s value in eq.2 for finding value of x.) Elimination by EQUATING THE CO-EFFICIENT (By making coefficient of any variable equal and subtracting the equations.)

CROSS MULTIPLICATION METHOD : 2/6/2009 DK Arya 5 CROSS MULTIPLICATION METHOD If equations are in General Form :- a1x+b1y+c1=0 ………..eq (1) a2x+b2y+c2=0 ………..eq (2) x={b1c2-b2c1}/{a1b2-a2b1} y={c1a2-c2a1}/{a1b2-a2b1}