Linear Equations in Two Variables Class 9 PPT

 Page 1


LINEAR EQUATION 
IN TWO VARIABLES
Page 2


LINEAR EQUATION 
IN TWO VARIABLES
System of equations or 
Simultaneous equations
A pair of linear equations in two variables 
is said to form a system of simultaneous 
(together) linear equations.
For Example, 2x – 3y + 4 = 0
x + 7y – 1 = 0
Form a system of two linear equations in 
variables x and y.
Page 3


LINEAR EQUATION 
IN TWO VARIABLES
System of equations or 
Simultaneous equations
A pair of linear equations in two variables 
is said to form a system of simultaneous 
(together) linear equations.
For Example, 2x – 3y + 4 = 0
x + 7y – 1 = 0
Form a system of two linear equations in 
variables x and y.
The general form of a linear equation in two 
variables x and y is 
ax + by + c = 0 , a = or not = 0, b= or not= 0, 
where
a, b and c being real numbers.
A solution of such an equation is a pair of values, 
one for x and the other for y, which makes two 
sides (LHS AND RHS) of the equation equal.
Every linear equation in two variables has 
infinitely many solutions which can be 
represented on a certain line.
Page 4


LINEAR EQUATION 
IN TWO VARIABLES
System of equations or 
Simultaneous equations
A pair of linear equations in two variables 
is said to form a system of simultaneous 
(together) linear equations.
For Example, 2x – 3y + 4 = 0
x + 7y – 1 = 0
Form a system of two linear equations in 
variables x and y.
The general form of a linear equation in two 
variables x and y is 
ax + by + c = 0 , a = or not = 0, b= or not= 0, 
where
a, b and c being real numbers.
A solution of such an equation is a pair of values, 
one for x and the other for y, which makes two 
sides (LHS AND RHS) of the equation equal.
Every linear equation in two variables has 
infinitely many solutions which can be 
represented on a certain line.
GRAPHICAL SOLUTIONS OF A LINEAR 
EQUATION
•Let us consider the following system of two 
simultaneous linear equations in two variable.
2x – y = -1
3x + 2y = 9
Here we assign any value to one of the two 
variables and then determine the value of the 
other variable from the given equation.
Page 5


LINEAR EQUATION 
IN TWO VARIABLES
System of equations or 
Simultaneous equations
A pair of linear equations in two variables 
is said to form a system of simultaneous 
(together) linear equations.
For Example, 2x – 3y + 4 = 0
x + 7y – 1 = 0
Form a system of two linear equations in 
variables x and y.
The general form of a linear equation in two 
variables x and y is 
ax + by + c = 0 , a = or not = 0, b= or not= 0, 
where
a, b and c being real numbers.
A solution of such an equation is a pair of values, 
one for x and the other for y, which makes two 
sides (LHS AND RHS) of the equation equal.
Every linear equation in two variables has 
infinitely many solutions which can be 
represented on a certain line.
GRAPHICAL SOLUTIONS OF A LINEAR 
EQUATION
•Let us consider the following system of two 
simultaneous linear equations in two variable.
2x – y = -1
3x + 2y = 9
Here we assign any value to one of the two 
variables and then determine the value of the 
other variable from the given equation.
For the equation
2x –y = -1 ---(1)
Solve for y
ADD 1 and add y to both sides
2x +1 = y
Switching sides
Y = 2x + 1
3x + 2y = 9 --- (2)
Solve for y
Subtract 3x on both sides
2y = 9 – 3x
Divide by 2 on both sides
y=(9-3x)/(2)
X        0          2
Y        1          5
X      3          -1
Y      0          6