A relationship between quantities can be described in more than one way. Some ways are more helpful than others, depending on what we want to find out. Let’s look at the angles of an isosceles triangle, for example.

Suppose we want to find $a$ when $b$ is $20^{\circ}$.  

Now suppose the bottom two angles are $34^\circ$ each. How many degrees is the top angle?

Notice that when $b$ is given, we did the same calculation repeatedly to find $a$: We substituted $b$ into the first equation, subtracted $b$ from 180, and then divided the result by 2. 

Instead of taking these steps over and over whenever we know $b$ and want to find $a$, we can rearrange the equation to isolate $a$:

$\begin{aligned} a + a + b &= 180\\ 2a + b&=180\\2a &=180-b\\ a &=\dfrac{180-b}{2} \end{aligned}$

This equation is equivalent to the first one. To find $a$, we can now simply substitute any value of $b$ into this equation and evaluate the expression on the right side.

Likewise, we can write an equivalent equation to make it easier to find $b$ when we know $a$:

$\begin{aligned} a + a + b &= 180\\ 2a + b&=180\\b &=180-2a \end{aligned}$

Rearranging an equation to isolate one variable is called solving for a variable. In this example, we have solved for $a$ and for $b$. All three equations are equivalent. Depending on what information we have and what we are interested in, we can choose a particular equation to use.