# How do you simplify (63x + 6y) + (-16x + 46y) ?

Sep 20, 2015

$47 x + 52 y$

#### Explanation:

"You'll have to count apples as apples and oranges as oranges."
In this case, the apples would be the x, and the oranges would be the y (or vice versa).

Well, in other words, you cannot add x and y together because they are two different things, so just leave them separate.

Anyway, it is just a matter of opening the parentheses and do simple additions.
Remember the rules:
$\left(a + b\right) = a + b$
$- \left(a + b\right) = - a - b$
$- \left(a - b\right) = - a + b$

Let's open all those parentheses without any worry of changing signs in this case.

Note: the MINUS sign here is associated to the number 16. It is really just (-16). The sign outside the parentheses are all +.

So, we have:
$\left(63 x + 6 y\right) + \left(- 16 x + 46 y\right)$
$= 63 x + 6 y - 16 x + 46 y$

Now we have to count the x together and the y together.
We group them together (it's easier to see) and have:
$= 63 x - 16 x + 6 y + 46 y$
Here, you see, we are gathering the apples (x) and the oranges (y) together.
You could factor out the x and y and rewrite this as follow:
$= \left(63 - 16\right) x + \left(6 + 46\right) y$
if it makes you feel more comfortable doing the addition (subtraction).

Finally,
$63 - 16 = 47$ and
$6 + 46 = 52$
so we have
$\left(63 x + 6 y\right) + \left(- 16 x + 46 y\right) = 47 x + 52 y$

which cannot be simplified further.

That's it. Hope it helped.