CREATED BY- ANKIT VYAS CLASS- X B ROLL NO.- 35

LINEAR EQUATION IN 2 VARIABLES

An equation of the form ax + by +c = O or ax + by = c , where a ,b ,c are real numbers , a and b ≠ O and x , y are variables , is called a linear equation in two variables.

WHAT ARE VARIABLES? It is a symbol that represents a

quantity in an algebraic expression for ex- x , y , a , b , h . d , j etc.

WHAT ARE SOLUTIONS? Let ax + by +c = O , where a ,b , c

are real numbers such that a and b ≠ O. Then, any pair of values of x and y which satisfies the equation ax + by +c = O, is called a solution of it.

ILLUSTRTION 1 :- X = 3, Y = 2 IS A SOLUTION OF 3X-2Y=5 BECAUSE WHEN X=3 , Y=2, WE HAVE:LHS = 3X3-2X2=5=RHS. BUT X=3 AND Y=-2 IS NOT ITS SOLUTION, BECAUSE 3X3-2X-2 ≠5 I.E LHS≠RHS WHEN X=3 AND Y=-2.

ILLUSTRATION 2:- SHOW THAT (X=1, Y=1) AS WELL AS (X=2, Y=5) IS A SOLUTION OF 4X-Y-3=O. SOL. IF WE PUT X=1 AND Y=1 IN THE GIVEN EQUATION, WE HAVELHS = 4X1-1-3=O=RHSSO, X=1, Y=1 IS A SOLUTION OF 4X-Y-3=O.IF WE PUT X=2, Y=5 IN THE EQUATION 4X-Y-3=O , WE HAVE LHS = 4X2-5-3=O=RHSSO ,X=2, Y=5 IS A SOLUTION OF 4X-Y-3=O.

GRAPH OF A LINEAR EQUATION IN TWO VARIABLES

EX 1-Consider the linear equation x+4y=8. the solutions of the above equation are displayed below.

x = 0 8 4 -4 12 16 y = 2 0 1 3 -1 -2

Series1

-5 0 5 10 15 20

-3

-2

-1

0

1

2

3

4

Y

Y

-4,3

0,2

4,18,0

12,-1

16,-2

EX-2 CONSIDER THE LINEAR EQUATION 2X+Y=6.THE SOLUTIONS ARE AS FOLLOWS:

X= 0 8 -1 -2 4 Y= 6 -10 8 10 -2

0

Series1

-4 -2 0 2 4 6 8 10

-15

-10

-5

0

5

10

15

Y

Y

-2,10-1,80,6

4,-2

8,-10