Understanding Pair of Linear Equations in Two Variables
Explore the concept of pair of linear equations in two variables, graphical methods for solution, types of solutions, and the substitution method through detailed explanations and examples. Learn how to determine consistency, inconsistency, and dependence of linear equations, with practical applications and visual representations.
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Presentation Transcript
TOPIC : PAIR OF LINEAR EQUATIONS IN TWO VARABLES
INTRODUCTION An equation which can be put in the form of ax+by+c=0 , where a , b and c are real number and a and b are not both zero, is called a linear equation in two variable. Every solution of the equation is a point on the line representing it, each solution x and y of a linear equation in two variables, ax +by+c=0 corresponds to a point on the line representing the equation vice verse.
Possibilities Happen Two lines in a plane The given two lines in a plane, only one of the following three possibilities : i) The two lines will intersect a one point . ii) The two lines will not intersect.(i.e.)there are parallel. iii) The two lines will be coincident.
Graphical Method of Solution of a Pair of Linear Equations The equation representing the situation are geometrically shown by two lines intersecting at a point (4,2). Therefore , the point (4,2) lies on the lines representing by both the equations x-2y=0 and 3x+4y=20. And this is only common point . since (4,2) is only common point on both the lines , there is one and only one solution for this pair of liner equations in to variables .
Inconsistent consistent and dependent pair of linear equations A pair of linear equations has no solution is called an inconsistent pair of linear equation . A pair of linear equations in two variables , which has a solution is called a consistent pair of linear solution . A pair of linear equation which are equivalent has infinitely many distinct common solution this type linear equation called dependent linear equation.
Substitution method Let us we solve the following a pair of linear equations by substitution method : 7x-15y=2 , x+2y=3 Step 1: We pick either of the equation and write one variables in the term of the other. Let us consider the equation (2): x+2y=3 x=3-2 y Step2: substitute the value of x in equation (1). We get 7(3-2y)-15y=2 -29y=-19 Y=19\29 Step3: substituting the value of y in equation (3),so we get x=3-2(19/19)=49/29 So the value of x=49/29 and y=19/29
SANJAY KUMAR SINHA K V JEHANABAD JEHANABAD
