# The Solution of an Equation

## Definition

The Solution of an Equation: The value of the variable in an equation which satisfies the equation is called a solution to the equation.

## Notes

### The Solution of an Equation:

• The value of the variable in an equation which satisfies the equation is called a solution to the equation.

• The LHS of an equation is equal to its RHS only for a definite value of the variable in the equation. We say that this definite value of the variable satisfies the equation. This value itself is called the solution of the equation.

• For getting the solution of an equation, one method is the trial and error method. In this method, we give some value to the variable and check whether it satisfies the equation. We go on giving this way different values to the variable until we find the right value which satisfies the equation.

 Sr.NO. Equation Value of Variable Equation satisfied Yes/No 1 10y = 80 y = 10 No 2 10y = 80 y = 8 Yes 3 10y = 80 y = 5 No

## Example

Four years ago, Diljit was 8 years old. How old is he today?

Let us suppose he is a years old today.
Now, let’s write the given information using a.
a - 4 = 8
∴ a - 4 + 4 = 8 + 4..............(Adding 4 to both sides)
∴ a + 0 = 12
∴ a = 12
∴ Diljit is 12 years old today.

## Example

Jasmine has some money. Mother gave her 7 rupees. Jasmine now has 10 rupees. How much did she have to start with?

Let us suppose Jasmine had y rupees.

∴ y + 7 = 10

∴ y + 7 - 7 = 10 - 7

∴ y + 0 = 3

∴ y = 3

It means that Jasmine had 3 rupees to start with.

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What Is The Solution Of An Equation? [00:11:06]
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