31-03-2014, 12:08 PM
LINEAR EQUATION IN TWO VARIABLES
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Definition of a Linear Equation
A linear equation in two variable x is an equation that can be written in the form ax + by + c = 0, where a ,b and c are real numbers and a and b is not equal to 0.
example of a linear equation in x is .
ELIMINATION METHOD
In this method, we eliminate one of the two variables to obtain an equation in one variable which can easily be solved. Putting the value of this variable in any of the given equations, the value of the other variable can be obtained.
For example: we want to solve,
3x + 2y = 11
2x + 3y = 4
Let 3x + 2y = 11 --------- (i)
2x + 3y = 4 ---------(ii)
Multiply 3 in equation (i) and 2 in equation (ii) and subtracting eq iv from iii, we get
9x + 6y = 33 ------ (iii)
4x + 6y = 8 ------- (iv)
5x = 25
=> x = 5
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.