Processing math: 100%

Solution of an Equation

A solution of an equation is a value of the unknown variable that satisfy the equation.

A number, which when substituted for the variable in an equation makes its L.H.S equal to the R.H.S, is said to satisfy the equation and is called a solution of the equation.

Solving an Equation by Trial and Error Method:

Finding the solution of an equation is called solving the equation.

Trial and Error Method is used to solve an equation (linear equation).

Working Rules for this method are given below.


Working Rules for Solving an Equation by Trial and Error Method:

Step I: Take any equation.

Step II: Put several values of the variable and find the values of L.H.S and R.H.S. of the equations.

Step III: When for a particular value of the variable, L .H.S = R.H.S, then that value of the variable is solution of the equation.


Solved Example on Trial and Error Method:

1. Using trial and error method, find the solution of 5z = 10

Solution:

The given equation is 3z = 12

Since R. H.S. of the this equation is 12, therefore, we put several values of z to find L.H.S till for a particular value of z, it becomes equal to 12.

z

L.H.S.

R.H.S.

1

3 × 1 = 3

12

2

3 × 2 = 2

12

3

3 × 3 = 9

12

4

3 × 4 = 12

12

Thus, z = 4 is the solution of the given equation.


Direct Way of Solving an Equation
(Solving an Equation by The Method of Transposition):

Trial and error method is not a direct and practical way for finding a solution. We shall now look for a direct way of solving an equation i.e., finding the solution of the equation.


Working Rules for Direct Way of Solving an Equation:

To Solve an Equation by the Method of Transposition

Step I: Add the same number or quantity to each side of the equation without upsetting the balance of the equation.

Step II: Subtract the same number or quantity from each side of the equation without upsetting the balance of the equation.

Step III: Transfer (or transpose) any number or quantity from one side of the equation to the other side by changing its sign i.e., + to -or - to +.

Step IV: Multiply or divide both sides of the equation by the same number or quantity without upsetting the balance of the equation.

Step V: Transfer (or transpose) the numerical coefficient of any quantity at L.H.S. to R.H.S. as its denominator whereas the denominator of the L.H.S. gets transposed to R.H.S. as its numerator.


Solved Example on Direct Method to Solving an Equation:

1. Solve x + 6 = 23

Solution:

Adding -6 (the additive inverse of +6) to both the sides, we get

x + 6 - 6 = 23 - 6

or, x = 17

or, x = 17 is the required solution. 


2. If 9t = 63 then find the value of t.

Solution:

To find the value of t, eliminate its numerical coefficient of 9 by multiplying both the sides of the equation by 19

So, 9 × t × 19 = 63 × 19 

or, t × 1 = 7 × 1

or, t = 7

Hence, t = 7 is the solution of the equation 9t = 63.



Algebra Page

6th Grade Page

From Solution of an Equation to HOME PAGE



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More