SOLUTION: The difference of two numbers is 86. The second is 6 less than 5 times the first. What are the two numbers?

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Question 112043: The difference of two numbers is 86. The second is 6 less than 5 times the first. What are the two numbers?
Found 2 solutions by jim_thompson5910, BrittanyM:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let x=1st # and y=2nd #

Translate the following:

"The difference of two numbers is 86" becomes

"The second is 6 less than 5 times the first" becomes

Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute the negative

Combine like terms on the left side

Subtract 6 from both sides

Combine like terms on the right side

Divide both sides by -4 to isolate x

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and

Answer by BrittanyM(80) (Show Source):
You can put this solution on YOUR website!
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