PROJECT REPORT ON LINEAR EQUATION IN TWO VARIABLES 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
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