# Question #55694

Aug 22, 2016

They combined the like terms.

#### Explanation:

Let's begin at $\frac{16}{9} {y}^{2} + {y}^{2} = 25$. We can see that both terms on the left have a ${y}^{2}$:
$\frac{16}{9} \textcolor{red}{{y}^{2}} + \textcolor{red}{{y}^{2}} = 25$

Recall from algebra that we can combine these like terms. It's the same idea as this:
$x + x + x = 9$
$3 x = 9 \to x = 3$

You can add the three $x$s together to get $3 x$. In your example, we're going to add the $\frac{16}{9} {y}^{2}$ and the ${y}^{2}$ together:
$\frac{16}{9} {y}^{2} + {y}^{2} = 25$
$\frac{16 {y}^{2}}{9} + \frac{9 {y}^{2}}{9} = 25$ ($\frac{16}{9} {y}^{2}$ and $\frac{16 {y}^{2}}{9}$ are the same thing)
$\frac{25 {y}^{2}}{9} = 25$ or $\frac{25}{9} {y}^{2} = 25$

As you can see, we just added the fractions.