Question 112043
With the information which we have been given, we can set up equations to solve for the variables.


The difference of the two numbers is 86:
-x + y = 86


The second is 6 less than 5 times the first:
y = 5x - 6


we can put these together as a system:
-x + y = 86
5x - y = 6


By using the elimination method, we  have
4x = 92
x = 23


Now using the method of substitution, we can plug 23 into one of the equations to find y.


-(23) + y = 86
y = 109


We can check our answer by plugging both values in for x and y.  


-(23) + (109) = 86
86 = 86


5(23) - (109) = 6
6 = 6


Both of these statements are true, 
x = 23 
y = 109