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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

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