Question 18311
 x +y = 15  (the sum of two numbers is 15.
3x = 5y-11 ( three times one of the numbers is 11 less than five times the other).

Multiply the first equation by -3.

-3x - 3y = -45.
Rewrite the second equation as 

3x - 5y = -11.

Add these two equations:

-8y = -56
Divide both sides by -8.
y = 7.
Now, plug in this value in the first equation(x+y=15).

x + 7 = 15.
x = 8
Therefore the two numbers are 7 and 8.