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 112068: The difference of two numbers is 86. The second is 6 less than 5 times the first. What are the two numbers?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
y-x=86
y=5x-6



%285x-6%29-x=86 Plug in y=5x-6 into the first equation. In other words, replace each y with 5x-6. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


5x-6-x=86 Distribute


4x-6=86 Combine like terms on the left side


4x=86%2B6Add 6 to both sides


4x=92 Combine like terms on the right side


x=%2892%29%2F%284%29 Divide both sides by 4 to isolate x



x=23 Divide




Now that we know that x=23, we can plug this into y=5x-6 to find y



y=5%2823%29-6 Substitute 23 for each x


y=109 Simplify


So our answer is x=23 and y=109