Math question explanation

if x-y=11 and x^2-y^2=22, what is 5x+5y?

I know the answer is 10... can you please explain how you got the answer cause i don't get it. thanks!

x^2-y^2=22 is a difference of 2 squares which means its equivalent to saying:
(x-y)(x+y)=22
You're given that x-y=11 so substitute that in there:
11(x+y)=22
So x+y=2
5x+5y is equal to 5(x+y) so substitute in the "2" that you got and you have 5*2=10

I'm going to use substitution, but there are many ways to solve this.
Solve for x (or y if you want) in the 1st equation:
x - y = 11
x = y + 11

Now plus "y + 11" in for x in the 2nd equation:
(y + 11)^2 - y^2 = 22
y^2 + 22y + 121 - y^2 = 22
y^2 - y^2 + 22y = -99
22y = -99
y = -4.5

Plus -4.5 in for y in the 1st equation to solve for x:
x - (-4.5) = 11
x + 4.5 = 11
x = 6.5

Now plug 6.5 in for x and -4.5 in for y in your 5x + 5y equation:
5(6.5) + 5(-4.5) = 10

Hope this helped!

...from (x^2 - y^2) = 22
factor

(x + y)(x - y) = 22
(x - y) = 11
so,
(x + y) * 11 = 22
(x + y) = 2

5x + 5y = 5(2) = 10
too easy !