How to Solve Linear Equations
What is a linear equation: An How to Solve Linear Equations
equation is a condition on a variable. A
variable takes on different values; its value is not fixed . Variables are denoted usually by letter of alphabets,
such as x, y , z , l , m , n , p etc. From variables we form expression.
Linear equation in one variable : These are the type of equation which have unique (i.e, only one and one )
For example: 2 x + 5 = 0 is a linear equation in one variable.
Root of the equation is -52
Example 1: Convert the following equation in statement form.
x - 5 = 9
5 taken from x gives 9
So x = 9 + 5 = 14
Hence x = 14
For verification of the statement, How to Solve Linear Equations
x - 5 = 9
14 - 5 = 9
9 = 9 So left hand side value is equal to right hand side value.
Hence the value of x determined is correct .
You can try out some more examples from linear equations worksheets
Solving Linear Equations Examples
Below are few examples of equations which will help you to understand better how to solve linear equations:
Example of linear equations in one variable:
Example1: Solve 3n + 7 =25
Solution1: Given equation is 3n +7 = 25
Step1: Subtract 7 from both sides
3n+7-7 = 25-7
3n = 18
Step 2: Divide both side by 3 How to Solve Linear Equations
3n3 = 183
n = 6
Example of algebra linear equations in two variables
Example2: Find two different solutions of the equations.
(i) 4x + 3y = 12
(i ) 2x + 5y = 0
Solution 1: Let us take x=0, we get 3y = 12
i.e , y =4, So (0, 4 ) is a solution of the given equation.Similarly , by taking y=0 , we get x =3, thus , (3, 0) is
also a solution.
Two different solutions are (0,4) and (3,0)
Solution2:Let us take x=0 , we get 5y = 0, i.e y=0.
So (0,0) is a solution of a given equation.To get another solution , take x=1 , so corresponding value of y is
-25. So (1, -25) is second solution.
Two different solutions are (0,0) and (1, -25).