linear Equation
(basic concept is linear polynomial=0 is linear Equation)
- linear equation in one variable
- linear equation in two variable
Linear Equation in one variable
(one variable - In this case term of the variable is use to one means x or y or z etc.)
The standard form linear Euqation in one variable is (ax + b)=0
(In this Euation x is variable term and a is coefficient of x and b is constant.)
where a and b are real number.
Example:-
5x + 6 =0 , 6x + 7=0 , 9x + 6 =0 etc.
linear equation in two variable
(two variable - In this case term of the variable is use to two means x and y or other two variable etc.)
The standard form linear Euqation in two variable is (ax + by + c)=0
(In this Euation x and y is two variable term and a is coefficient of x and b is coefficient of y and c is constant.)
where a, b , c are real number.
Example:-
5x +2y + 6 =0 , 6x +9y + 7=0 , 9x +4y + 6 =0 etc.
pair of linear Equation
- Pair of linear Equation in one variable
- Pair of linear Equation in two variable
Pair of linear Equation in one variable
The standard form pair of linear Euqation in one variable is
(a1x + b1)=0
(a2x + b2)=0
(In this Euation x is variable term and a1 and a2 is coefficient of x in both pair of Equation and b1 and b2 constant.)
where a and b are real number.
Example:-
1.
5x + 6 =0
6x + 7=0 ,
2.
9x + 6
3x+5=0 etc.
Pair of linear Equation in two variable
The standard form pair of linear Euqation in one variable is
a1x + b1y+c1=0
a2x + b2y+c2=0
(In this Euation x and y is variable term and a1 and a2 is coefficient of x in both pair of Equation and b1 and b2 coefficient of x and y in both pair of Equation and c1 and c2 constant.)
where a and b are real number.
Example:-
1.
5x + 6y +3=0
6x + 8y + 7=0
2.
9x+3y + 6 =0
3x + 8y+5=0 etc.
In this chapter we discuss about pair of linear equation in two variable.
System of linear Equation in two variables
A system formed by taking two or more equations in two variables together is called a system of linear-equations
5x + 6y +3=0
6x + 8y + 7=0
Graph of linear Equation ax + by + c =0
Given linear Equation is ax + by + c =0 ..........(1)
case 1 when c ≠ 0
from (1), y=(-c-ax)/b
put in y=0 we get x=-c/a
coordinate point =(-c/a ,0)
again,
put in x=0 we get y=-c/b
ordinate point =(0 ,-c/b)
