Question 527770
Let x be the larger number and y be the smaller number  
Then:

x+y = 13
2x+2 = 5y

We have a system of equations so we can use either the elimination method or substitution method.

Since we have a coefficient of 1 on the first equation, let's use the substitution method.

x+y = 13  ---->  y = 13-x
2x+2 = 5y

Substitute 13-x where you see y.

2x + 2 = 5(13-x)
2x + 2 = 65 - 5x

7x = 63 

x = 9

Substitute x=9 back into either original equation.

9 + y = 13

y = 4

Thus our two numbers are 9 and 4.