Introduction to Algebraic Identities

Raj bought $5$ notebooks and $2$ pens and paid $110$ rupees to the shopkeeper.

If the price of one notebook is $x$ rupees and the price of one pen is $y$ rupees.

Then we can describe the situation mathematically as shown.

This is called a linear equation in $x$ and $y$.

Only a specific value of $x$ and $y$ will satisfy the above equation.

Also, the values of $x$ and $y$ depend on each other.

Shown above is also an equation in $a$ and $b$

For the above equation, any value of $a$ and $b$ will satisfy the equation.

Also, the value of $a$ and $b$ don't depend on each other.

An equation that holds true for any value of the variables is called identity.

Here are some identities that can be tested for any value of the variables.

An identity is an equality that holds good for any value of its variables.

But an equation is true only for some specific values of its variables.

For instance, let’s take an equation as shown.

This equation is true only if $x=5$ or $x=-12$

The equation is not true for any other value of $x$

Therefore this equation is not an identity.

Now, let’s consider the equation.

Let’s check this for different values of $a$ and $b$

So this is an identity, as it holds true for every value of $a$ and $b$

Revision

An identity is an equation true for every value of the variable.

An equation is true for only certain values of variables but not for all values of variables.

The End