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Home >> Polynomials >> Linear Equations >>

Linear Equations

Linear Equation in one Variable Linear Equation in Two Variables Difference between Linear Equation in One & Two Variables Linear Expression Linear Equations Complex Examples
Solving a Pair of Linear Equations

Linear Equations are those which have only Linear Polynomials i.e. 1 is the highest degree of term in a given polynomial it is called Linear Polynomial.

An example equation of Linear Polynomial is: 5x + 3

If the highest degree is 2 or 3 it is called Quadratic and Cubic Polynomials Equations. To know more about the concept of Linear, Quadratic and Cubic you can read Degree of Polynomials

Solving Linear Equation - means finding value of a variable which can satisfy the given equation is called solution of the equation

Let's take an example of linear equation

Example : 5x - 2 = 18
Step are as follows -
5x = 18 + 2
Or 5x = 20
Or x = 20 / 5
x = 4

Now, we can add the value of x to verify the equation and find out whether LHS = RHS

LHS = 5x - 2
LHS = (5 X 4) - 2
LHS = 20 - 2
LHS = 18

RHS = 18

So, LHS = RHS

Let's study some more examples and verify whether the given value of variable is a solution to the equation

Example - 1 : Solve Equation y + 4 = 2y and verify whether LHS = RHS
Solution : Steps to solve this equation are as follows -
y + 4 = 2y
or 2y - y = 4
or y = 4

Now, we can add the value of y to verify the equation and find out whether LHS = RHS

LHS = y + 4
LHS = 4 + 4
LHS = 8

RHS = 2y
RHS = 2 X 4
RHS = 8

So, LHS = RHS

Example - 2 : Solve Equation 3y + 3 = 15 and verify whether LHS = RHS
Solution : Steps to solve this equation are as follows -
3y + 3 = 15
3y = 15 - 3
3y = 12
y = 12 / 3
y = 4

Now, we can add the value of y to vertify the equation and find out whether LHS = RHS

LHS = 3y + 3
LHS = (3 X 4) + 3
LHS = 12 + 3
LHS = 15

RHS = 15

So, LHS = RHS

Example - 3 : Solve 5x + 5 = 7 + 4x
Solution : steps are as follows -

5x + 5 = 7 + 4x
5x - 4x = 7 - 5
x = 2
Hence 2 is the solution

Example - 4 : Solve 2( y- 5) = 3(y + 2) - 2
Solution : steps are as follows -

2(y- 5) = 3(y + 2) - 2
2y - 10 = 3y + 6 - 2
2y - 3y = 6 - 2 + 10
-y = 4 + 10
-y = 14
y = -14